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## King, John Robert

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 Author ID: king.john-robert Published as: King, J. R.; King, John; King, John R.; King, John Robert Homepage: https://www.nottingham.ac.uk/mathematics/people/john.king External Links: MGP · ORCID
 Documents Indexed: 266 Publications since 1986 Biographic References: 1 Publication
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#### Co-Authors

 36 single-authored 15 Byrne, Helen Mary 15 Ward, John Paul 12 Meere, Martin G. 11 Riley, David S. 10 Evans, Jonathan David 9 Jabbari, Sara 8 Galaktionov, Victor Aleksandrovich 8 Loose, Matthew 7 Bennett, Malcolm J. 7 Cherniha, Roman M. 7 Koerber, Adrian J. 6 Bowen, Mark 6 Chapman, Stephen Jonathan 6 Dalwadi, Mohit P. 6 Fila, Marek 6 Franks, Susan J. 6 Hulshof, Josephus 6 Lemon, Greg 6 McCue, Scott William 6 Wattis, Jonathan A. D. 5 Bokes, Pavol 5 Croft, Julie M. 5 Howison, Sam D. 5 Jensen, Oliver E. 5 Minton, Nigel P. 5 Rogers, Tryfan G. 5 Sockett, R. Elizabeth 5 Tew, Richard H. 5 Winkler, Michael 4 Bridge, Lloyd J. 4 Cox, Steven M. 4 Daskalopoulos, Panagiota 4 Hill, S. J. 4 Middleton, Alistair M. 4 Münch, Andreas 4 Ockendon, John R. 4 O’Dea, Reuben D. 4 Taranets, Roman M. 4 Tuck, Brian 4 Yanagida, Eiji 3 Anguige, Keith 3 Cummings, Linda J. 3 Fozard, John A. 3 Muraro, Daniele 3 Noakes, Caroline J. 3 Owen, Markus Roger 3 Please, Colin P. 3 Sesum, Natasa 3 Thorn, Graeme J. 3 van den Berg, Jan Bouwe 3 Ward, Michael J. 3 Waters, Sarah Louise 3 Wood, Andrew T. A. 3 Woodroffe, P. J. 2 Adams, K. L. 2 Brown, Laura E. 2 Chen, Chiao-Yi 2 Chugunova, Marina A. 2 Cuesta Romero, Carlota Maria 2 Daalhuis, A. B. Olde 2 Davies, Susan C. 2 Dean, Andrew D. 2 Del Pino, Manuel A. 2 Dunster, Joanne L. 2 Evans, G. S. 2 Evans, P. L. 2 Flitton, J. C. 2 Heap, John T. 2 Hilhorst, Danielle 2 Lacey, Andrew A. 2 Macdonald, Ian A. 2 Matthews, Paul Charles 2 Mazzatti, Dawn J. 2 Mellor, Nathan 2 Mirams, Gary R. 2 Oliver, James M. 2 Oliver, Jonathan M. 2 Pearson, Taliesin 2 Richardson, Giles 2 Röger, Matthias 2 Rose, Felicity R. A. J. 2 Sansom, Ahmos 2 Sharp, T. E. 2 Smith, Warren R. 2 Wagner, Barbara A. 2 Wallman, A. M. 2 Whiteley, Jonathan P. 2 Williams, Paul Anthony 2 Williams, Paul J. 2 Williams, Paul T. 1 Abdulla, Ugur G. 1 Addison, J. A. 1 Allen, E. D. 1 Band, Leah R. 1 Bernis, Francisco 1 Betelú, Santiago I. 1 Blowey, James F. 1 Bluman, George W. 1 Body, Giles L. 1 Broadbridge, Philip ...and 103 more Co-Authors
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#### Serials

 26 European Journal of Applied Mathematics 22 Journal of Engineering Mathematics 20 Journal of Mathematical Biology 17 SIAM Journal on Applied Mathematics 16 Bulletin of Mathematical Biology 15 Quarterly Journal of Mechanics and Applied Mathematics 14 Mathematical Biosciences 13 IMA Journal of Applied Mathematics 12 Journal of Physics A: Mathematical and General 10 Nonlinearity 10 Mathematical Medicine and Biology 10 Journal of Theoretical Biology 5 IMA Journal of Mathematics Applied in Medicine and Biology 5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 3 Journal of Mathematical Analysis and Applications 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Mathematical and Computer Modelling 3 Mathematical Proceedings of the Royal Irish Academy 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Journal of Differential Equations 2 Studies in Applied Mathematics 2 Applied Mathematics Letters 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Advances in Differential Equations 2 Journal of Theoretical Medicine 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Interfaces and Free Boundaries 2 Networks and Heterogeneous Media 1 International Journal of Engineering Science 1 Journal of the Australian Mathematical Society, Series B 1 Wave Motion 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quarterly of Applied Mathematics 1 Physica D 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Philosophical Transactions of the Royal Society of London. Series A 1 Communications in Analysis and Geometry 1 Physics of Fluids 1 NoDEA. Nonlinear Differential Equations and Applications 1 Mathematical Research Letters 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Communications in Nonlinear Science and Numerical Simulation 1 Computer Assisted Mechanics and Engineering Sciences 1 AMRX. Applied Mathematics Research eXpress 1 SIAM Journal on Applied Dynamical Systems 1 Multiscale Modeling & Simulation 1 Complex Analysis and Operator Theory 1 Mathematical Modelling of Natural Phenomena 1 Symmetry 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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#### Fields

 148 Partial differential equations (35-XX) 101 Biology and other natural sciences (92-XX) 79 Fluid mechanics (76-XX) 27 Ordinary differential equations (34-XX) 21 Numerical analysis (65-XX) 21 Classical thermodynamics, heat transfer (80-XX) 17 Statistical mechanics, structure of matter (82-XX) 16 Dynamical systems and ergodic theory (37-XX) 12 Mechanics of deformable solids (74-XX) 7 Optics, electromagnetic theory (78-XX) 6 Differential geometry (53-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

215 Publications have been cited 1,721 times in 1,054 Documents Cited by Year
Mathematical modelling of avascular-tumour growth. Zbl 0866.92011
Ward, J. P.; King, J. R.
1997
A two-phase model of solid tumour growth. Zbl 1040.92015
Byrne, H. M.; King, J. R.; McElwain, D. L. S.; Preziosi, L.
2003
Two generalizations of the thin film equation. Zbl 1001.35073
King, J. R.
2001
Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation. Zbl 0943.92019
Ward, J. P.; King, J. R.
1999
Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. Zbl 1110.92016
Lemon, Greg; King, John R.; Byrne, Helen M.; Jensen, Oliver E.; Shakesheff, Kevin M.
2006
Self-similar behaviour for the equation of fast nonlinear diffusion. Zbl 0797.35097
King, J. R.
1993
Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures. Zbl 1014.92021
Ward, John P.; King, John R.
2003
Exact polynomial solutions to some nonlinear diffusion equations. Zbl 0779.35056
King, J. R.
1993
Modelling the early growth of ductal carcinoma in situ of the breast. Zbl 1050.92030
Franks, S. J.; Byrne, H. M.; King, J. R.; Underwood, J. C. E.; Lewis, C. E.
2003
Interactions between a uniformly proliferating tumour and its surroundings: Uniform material properties. Zbl 1044.92032
Franks, S. J.; King, J. R.
2003
Exact similarity solutions to some nonlinear diffusion equations. Zbl 0728.35052
King, J. R.
1990
The mesa problem: diffusion patterns for $$u_ t=\nabla \cdot (u^ m\nabla u)$$ as $$m\to +\infty$$. Zbl 0655.35034
Elliott, C. M.; Herrero, M. A.; King, J. R.; Ockendon, J. R.
1986
Unstable sixth-order thin film equation. I: Blow-up similarity solutions. Zbl 1173.35562
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Source-type solutions of the fourth-order unstable thin film equation. Zbl 1156.35387
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Asymptotic results for the Stefan problem with kinetic undercooling. Zbl 0998.80004
Evans, J. D.; King, J. R.
2000
Approximate solutions to a nonlinear diffusion equation. Zbl 0695.35103
King, J. R.
1988
Unstable sixth-order thin film equation. II: Global similarity patterns. Zbl 1173.35530
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Lie symmetries of nonlinear multidimensional reaction-diffusion systems. II. Zbl 1059.35058
Cherniha, Roman; King, John R.
2003
The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids. Zbl 0996.92013
Chen, C. Y.; Byrne, H. M.; King, J. R.
2001
Moving-boundary and fixed-domain problems for a sixth-order thin-film equation. Zbl 1105.76010
Flitton, J. C.; King, J. R.
2004
Exact multidimensional solutions to some nonlinear diffusion equations. Zbl 0818.35015
King, J. R.
1993
Nonlinear reaction-diffusion systems with variable diffusivities: Lie symmetries, ansätze and exact solutions. Zbl 1073.35115
Cherniha, Roman; King, John R.
2005
Moving boundary problems and non-uniqueness for the thin film equation. Zbl 0985.35113
King, J. R.; Bowen, M.
2001
Lie symmetries of nonlinear multidimensional reaction-diffusion systems. I. Zbl 0947.35026
Cherniha, Roman; King, John R.
2000
Two-dimensional Stokes and Hele-Shaw flows with free surfaces. Zbl 0955.76023
Cummings, L. J.; Howison, S. D.; King, J. R.
1999
Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations. Zbl 0916.34017
Chapman, S. J.; King, J. R.; Adams, K. L.
1998
Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population. Zbl 1091.92036
Anguige, K.; King, J. R.; Ward, J. P.
2005
Formal asymptotics of bubbling in the harmonic map heat flow. Zbl 1037.35023
van den Berg, Jan Bouwe; Hulshof, Josephus; King, John R.
2003
Stokes phenomenon and matched asymptotic expansions. Zbl 0834.41026
Olde Daalhuis, A. B.; Chapman, S. J.; King, J. R.; Ockendon, J. R.; Tew, R. H.
1995
Continuum approximations of individual-based models for epithelial monolayers. Zbl 1184.92011
Fozard, J. A.; Byrne, H. M.; Jensen, O. E.; King, J. R.
2010
Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2006
Persistence of corners in free boundaries in Hele-Shaw flow. Zbl 0840.76016
King, J. R.; Lacey, A. A.; Vazquez, J. L.
1995
Blow-up similarity solutions of the fourth-order unstable thin film equation. Zbl 1221.35296
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Beyond-all-orders effects in multiple-scales asymptotics: Travelling-wave solutions to the Kuramoto-Sivashinsky equation. Zbl 1044.76016
Adams, K. L.; King, J. R.; Tew, R. H.
2003
Mathematical modelling of quorum sensing in bacteria. Zbl 0998.92043
Ward, J. P.; King, J. R.; Koerber, A. J.; Williams, P.; Croft, J. M.; Sockett, R. E.
2001
Modelling the response of spatially structured tumours to chemotherapy: drug kinetics. Zbl 1130.92033
Norris, E. S.; King, J. R.; Byrne, H. M.
2006
A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm. Zbl 1101.92020
Anguige, K.; King, J. R.; Ward, J. P.
2006
The isolation oxidation of silicon: The reaction-controlled case. Zbl 0672.76095
King, J. R.
1989
Mathematical modelling of therapies targeted at bacterial quorum sensing. Zbl 1057.92033
Anguige, K.; King, J. R.; Ward, J. P.; Williams, P.
2004
Some non-local transformations between nonlinear diffusion equations. Zbl 0719.35042
King, J. R.
1990
Explicit solutions to six free-boundary problems in fluid flow and diffusion. Zbl 0673.76099
Howison, S. D.; King, J. R.
1989
Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression. Zbl 1303.92030
Bokes, Pavol; King, John R.; Wood, Andrew T. A.; Loose, Matthew
2012
Early development and quorum sensing in bacterial biofilms. Zbl 1038.92012
Ward, John P.; King, John R.; Koerber, Adrian J.; Croft, Julie M.; Sockett, R. Elizabeth; Williams, Paul
2003
Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents. Zbl 1019.35042
Galaktionov, Victor A.; King, John R.
2003
Exact solutions to a nonlinear diffusion equation. Zbl 0734.35087
King, J. R.
1991
On the Fisher-KPP equation with fast nonlinear diffusion. Zbl 1058.35110
King, John R.; McCabe, Philip M.
2003
Extinction behaviour for two-dimensional inward-solidification problems. Zbl 1041.35092
McCue, Scott W.; King, John R.; Riley, David S.
2003
Interface development and local solutions to reaction-diffusion equations. Zbl 0964.35086
Abdulla, Ugur G.; King, John R.
2000
Exact results for the nonlinear diffusion equations $$\partial u/\partial t=(\partial/\partial x)(u^{-4/3}\partial u/\partial x)$$ and $$\partial u/\partial t=(\partial/\partial x)(u^{-2/3}\partial u/\partial x)$$. Zbl 0760.35038
King, J. R.
1991
Type I ancient compact solutions of the Yamabe flow. Zbl 1338.53018
Daskalopoulos, Panagiota; del Pino, Manuel; King, John; Sesum, Natasa
2016
Multiscale stochastic modelling of gene expression. Zbl 1303.92067
Bokes, Pavol; King, John R.; Wood, Andrew T. A.; Loose, Matthew
2012
Mathematical modelling of the agroperon in staphylococcus aureus. Zbl 1202.92041
Jabbari, Sara; King, John R.; Koerber, Adrian J.; Williams, Paul
2010
Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosity. Zbl 1118.92024
Lemon, G.; King, J. R.
2007
On the development of rational approximations incorporating inertial effects in coating and rimming flows: a multiple-scales approach. Zbl 1090.76008
Noakes, C. J.; King, J. R.; Riley, D. S.
2006
Mathematical analysis of some multi-dimensional tissue-growth models. Zbl 1066.35038
King, J. R.; Franks, S. J.
2004
Cell-signalling repression in bacterial quorum sensing. Zbl 1055.92017
Ward, J. P.; King, J. R.; Koerber, A. J.; Croft, J. M.; Sockett, R. E.; Williams, P.
2004
The selection of Saffman-Taylor fingers by kinetic undercooling. Zbl 1028.76005
Chapman, S. J.; King, J. R.
2003
Fast diffusion equation with critical Sobolev exponent in a ball. Zbl 0988.35088
Galaktionov, Victor A.; King, John R.
2002
Asymptotics beyond all orders and Stokes lines in nonlinear differential-difference equations. Zbl 0999.34072
King, J. R.; Chapman, S. J.
2001
Asymptotic analysis of the steady-state and time-dependent Berman problem. Zbl 1009.76023
King, J. R.; Cox, S. M.
2001
Dipoles and similarity solutions of the thin film equation in the half-line. Zbl 0942.35094
Bernis, Francisco; Hulshof, Josephus; King, John R.
2000
Integral results for nonlinear diffusion equations. Zbl 0753.76168
King, J. R.
1991
Multiscale analysis of pattern formation via intercellular signalling. Zbl 1214.92006
O’Dea, R. D.; King, J. R.
2011
A multiple timescale analysis of a mathematical model of the Wnt/$$\beta$$-catenin signalling pathway. Zbl 1311.92094
Mirams, Gary R.; Byrne, Helen M.; King, John R.
2010
Mathematical modelling of the $$Aux/IAA$$ negative feedback loop. Zbl 1198.92005
Middleton, A. M.; King, J. R.; Bennett, M. J.; Owen, M. R.
2010
Small- and waiting-time behavior of the thin-film equation. Zbl 1178.35388
Blowey, James F.; King, John R.; Langdon, Stephen
2007
Regularization by kinetic undercooling of blow-up in the ill-posed Stefan problem. Zbl 1099.35178
King, J. R.; Evans, J. D.
2005
Thin-film flows near isolated humps and interior corners. Zbl 1074.76008
Jensen, O. E.; Chini, G. P.; King, J. R.
2004
Asymptotic behaviour of the thin film equation in bounded domains. Zbl 0971.76013
Bowen, M.; King, J. R.
2001
Scalar wave diffraction by tangent rays. Zbl 1074.76613
Tew, R. H.; Chapman, S. J.; King, J. R.; Ockendon, J. R.; Zafarullah, I.
2000
High concentration arsenic diffusion in crystalline silicon: An asymptotic analysis. Zbl 0812.35100
King, J. R.
1987
Exponential asymptotics of homoclinic snaking. Zbl 1241.35017
Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.
2011
Lie symmetries and conservation laws of nonlinear multidimensional reaction-diffusion systems with variable diffusivities. Zbl 1122.35053
Cherniha, Roman; King, John R.
2006
Linear stability of a ridge. Zbl 1124.76015
King, J. R.; Münch, A.; Wagner, B.
2006
The extinction problem for three-dimensional inward solidification. Zbl 1092.80007
McCue, Scott W.; King, John R.; Riley, David S.
2005
Surface-tension-driven dewetting of Newtonian and power-law fluids. Zbl 1073.76003
Flitton, J. C.; King, J. R.
2004
A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: quorum sensing and the build-up to invasion. Zbl 1334.92235
Koerber, A. J.; King, J. R.; Ward, J. P.; Williams, P.; Croft, J. M.; Sockett, R. E.
2002
Thin-film flows and high-order degenerate parabolic equations. Zbl 1077.76007
King, John R.
2001
Addendum: “Lie symmetries of nonlinear multidimensional reaction-diffusion systems. I. ”. Zbl 0978.35018
Cherniha, Roman; King, John R.
2000
The Smoluchowski coagulation equations with continuous injection. Zbl 0961.82024
Davies, Susan C.; King, John R.; Wattis, Jonathan A. D.
1999
On the behaviour of blow-up interfaces for an inhomogeneous filtration equation. Zbl 0869.35076
Galaktionov, V. A.; King, J. R.
1996
Local transformations between some nonlinear diffusion equations. Zbl 0768.35039
King, J. R.
1992
Diffusion of dopant and crystalline silicon: An asymptotic analysis. Zbl 0626.76094
King, J. R.; Please, C. P.
1986
Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085
Fila, M.; King, J. R.; Winkler, M.
2014
Thin-film modelling of biofilm growth and quorum sensing. Zbl 1398.76017
Ward, J. P.; King, J. R.
2012
Contracting bubbles in Hele-Shaw cells with a power-law fluid. Zbl 1215.35174
McCue, Scott W.; King, John R.
2011
Linear behaviour of solutions of a superlinear heat equation. Zbl 1263.35137
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2008
Mathematical analysis of a model describing the invasion of bacteria in burn wounds. Zbl 1117.35036
Hilhorst, D.; King, J. R.; Röger, M.
2007
Thin-film modelling of poroviscous free surface flows. Zbl 1112.76021
King, J. R.; Oliver, J. M.
2005
Thin-film theories for two-phase reactive flow models of active cell motion. Zbl 1069.92002
Oliver, J. M.; King, J. R.; McKinlay, K. J.; Brown, P. D.; Grant, D. M.; Scotchford, C. A.; Wood, J. V.
2005
Extinction behaviour of contracting bubbles in porous media. Zbl 1033.76058
McCue, S. W.; King, J. R.; Riley, D. S.
2003
The Laplace-Young equation near a corner. Zbl 0932.76012
King, J. R.; Ockendon, J. R.; Ockendon, H.
1999
New type I ancient compact solutions of the Yamabe flow. Zbl 1393.53058
Daskalopoulos, Panagiota; del Pino, Manuel; King, John; Sesum, Natasa
2017
The resolution of inflammation: a mathematical model of neutrophil and macrophage interactions. Zbl 1300.92018
Dunster, J. L.; Byrne, H. M.; King, J. R.
2014
On an unstable thin-film equation in multi-dimensional domains. Zbl 1302.35222
Taranets, Roman M.; King, John R.
2014
Buckling of a growing tissue and the emergence of two-dimensional patterns. Zbl 1308.92018
Nelson, M. R.; King, J. R.; Jensen, O. E.
2013
Grow up and slow decay in the critical Sobolev case. Zbl 1262.35032
Fila, Marek; King, John R.
2012
Continuum limits of pattern formation in hexagonal-cell monolayers. Zbl 1284.92024
O’Dea, R. D.; King, J. R.
2012
Similarity: Generalizations, applications and open problems. Zbl 1188.00015
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.
2010
Modelling the activation of G-protein coupled receptors by a single drug. Zbl 1187.92043
Woodroffe, P. J.; Bridge, L. J.; King, J. R.; Hill, S. J.
2009
A tractable mathematical model for tissue growth. Zbl 1442.35557
Eyles, Joe; King, John R.; Styles, Vanessa
2019
Extinction profile of complete non-compact solutions to the Yamabe flow. Zbl 07157605
Daskalopoulos, Panagiota; King, John; Sesum, Natasa
2019
Moving boundary problems for quasi-steady conduction limited melting. Zbl 1423.35469
Morrow, Liam C.; King, John R.; Moroney, Timothy J.; McCue, Scott W.
2019
Upscaling diffusion through first-order volumetric sinks: a homogenization of bacterial nutrient uptake. Zbl 1392.35317
Dalwadi, Mohit P.; Wang, Yanming; King, John R.; Minton, Nigel P.
2018
Multi-timescale analysis of a metabolic network in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine. Zbl 1392.92029
Dalwadi, Mohit P.; King, John R.; Minton, Nigel P.
2018
Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway. Zbl 1397.92281
Dalwadi, Mohit P.; Garavaglia, Marco; Webb, Joseph P.; King, John R.; Minton, Nigel P.
2018
New type I ancient compact solutions of the Yamabe flow. Zbl 1393.53058
Daskalopoulos, Panagiota; del Pino, Manuel; King, John; Sesum, Natasa
2017
The interface dynamics of a surfactant drop on a thin viscous film. Zbl 1375.35368
Chugunova, Marina; King, John R.; Taranets, Roman M.
2017
Mathematical modelling of thrombin generation: asymptotic analysis and pathway characterization. Zbl 1404.92082
Dunster, J. L.; King, J. R.
2017
Type I ancient compact solutions of the Yamabe flow. Zbl 1338.53018
Daskalopoulos, Panagiota; del Pino, Manuel; King, John; Sesum, Natasa
2016
Lie symmetry properties of nonlinear reaction-diffusion equations with gradient-dependent diffusivity. Zbl 07247533
Cherniha, Roman; King, John R.; Kovalenko, Sergii
2016
The metabolic network of Clostridium acetobutylicum: comparison of the approximate Bayesian computation via sequential Monte Carlo (ABC-SMC) and profile likelihood estimation (PLE) methods for determinability analysis. Zbl 1364.92013
Thorn, Graeme J.; King, John R.
2016
On contact-line dynamics with mass transfer. Zbl 1386.80004
Oliver, J. M.; Whiteley, J. P.; Saxton, M. A.; Vella, D.; Zubkov, V. S.; King, J. R.
2015
Lie and conditional symmetries of a class of nonlinear (1 + 2)-dimensional boundary value problems. Zbl 1375.35019
Cherniha, Roman; King, John R.
2015
The Hele-Shaw injection problem for an extremely shear-thinning fluid. Zbl 1387.76030
Richardson, G.; King, J. R.
2015
Mathematical modelling reveals properties of tcdc required for it to be a negative regulator of toxin production in clostridium difficile. Zbl 1314.34100
Jabbari, Sara; Cartman, Stephen T.; King, John R.
2015
Modelling of Arabidopsis LAX3 expression suggests auxin homeostasis. Zbl 1412.92188
Mellor, Nathan; Péret, Benjamin; Porco, Silvana; Sairanen, Ilkka; Ljung, Karin; Bennett, Malcolm; King, John
2015
Orientation-dependent pinning and homoclinic snaking on a planar lattice. Zbl 1370.37137
Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.
2015
Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085
Fila, M.; King, J. R.; Winkler, M.
2014
The resolution of inflammation: a mathematical model of neutrophil and macrophage interactions. Zbl 1300.92018
Dunster, J. L.; Byrne, H. M.; King, J. R.
2014
On an unstable thin-film equation in multi-dimensional domains. Zbl 1302.35222
Taranets, Roman M.; King, John R.
2014
Two different network topologies yield bistability in models of mesoderm and anterior mesendoderm specification in amphibians. Zbl 1412.92116
Brown, Laura E.; King, John R.; Loose, Matt
2014
A mathematical model of the human metabolic system and metabolic flexibility. Zbl 1300.92031
Pearson, T.; Wattis, J. A. D.; King, J. R.; MacDonald, I. A.; Mazzatti, D. J.
2014
Buckling of a growing tissue and the emergence of two-dimensional patterns. Zbl 1308.92018
Nelson, M. R.; King, J. R.; Jensen, O. E.
2013
Transcriptional bursting diversifies the behaviour of a toggle switch: hybrid simulation of stochastic gene expression. Zbl 1278.92009
Bokes, Pavol; King, John R.; Wood, Andrew T. A.; Loose, Matthew
2013
Multiple travelling-wave solutions in a minimal model for cell motility. Zbl 1272.92005
Kimpton, L. S.; Whiteley, J. P.; Waters, S. L.; King, J. R.; Oliver, J. M.
2013
pH-induced gene regulation of solvent production by Clostridium acetobutylicum in continuous culture: parameter estimation and sporulation modelling. Zbl 1402.92224
Thorn, Graeme J.; King, John R.; Jabbari, Sara
2013
The role of auxin and cytokinin signalling in specifying the root architecture of Arabidopsis thaliana. Zbl 1368.92071
Muraro, Daniele; Byrne, Helen; King, John; Bennett, Malcolm
2013
Dynamics of a viscous thread on a non-planar substrate. Zbl 1367.76008
Bowen, Mark; King, John R.
2013
Asymmetric travelling waves for the thin film equation. Zbl 1322.35050
King, John R.; Taranets, Roman M.
2013
The putative influence of the agr operon upon survival mechanisms used by clostridium acetobutylicum. Zbl 1281.92019
Jabbari, Sara; Steiner, Elisabeth; Heap, John T.; Winzer, Klaus; Minton, Nigel P.; King, John R.
2013
Wave pinning and spatial patterning in a mathematical model of antivin/lefty-nodal signalling. Zbl 1279.92016
Middleton, A. M.; King, J. R.; Loose, M.
2013
The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling. Zbl 1402.92056
O’Dea, R. D.; King, J. R.
2013
A functional differential equation model for biological cell sorting due to differential adhesion. Zbl 1257.92021
Lemon, Greg; King, John R.
2013
Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression. Zbl 1303.92030
Bokes, Pavol; King, John R.; Wood, Andrew T. A.; Loose, Matthew
2012
Multiscale stochastic modelling of gene expression. Zbl 1303.92067
Bokes, Pavol; King, John R.; Wood, Andrew T. A.; Loose, Matthew
2012
Thin-film modelling of biofilm growth and quorum sensing. Zbl 1398.76017
Ward, J. P.; King, J. R.
2012
Grow up and slow decay in the critical Sobolev case. Zbl 1262.35032
Fila, Marek; King, John R.
2012
Continuum limits of pattern formation in hexagonal-cell monolayers. Zbl 1284.92024
O’Dea, R. D.; King, J. R.
2012
Multiscale modelling of auxin transport in the plant-root elongation zone. Zbl 1303.92061
Band, L. R.; King, J. R.
2012
Cross-strain quorum sensing inhibition by staphylococcus aureus. II: A spatially inhomogeneous model. Zbl 1312.92019
Jabbari, Sara; King, John R.; Williams, Paul
2012
Cross-strain quorum sensing inhibition by staphylococcus aureus. I: A spatially homogeneous model. Zbl 1251.92007
Jabbari, Sara; King, John R.; Williams, Paul
2012
Uniqueness of the regular waiting-time type solution of the thin film equation. Zbl 1242.76041
Chugunova, Marina; King, John R.; Taranets, Roman M.
2012
A mathematical model of the bovine oestrous cycle: simulating outcomes of dietary and pharmacological interventions. Zbl 1337.92231
Pring, Stephen R.; Owen, Markus; King, John R.; Sinclair, Kevin D.; Webb, Robert; Flint, Anthony P. F.; Garnsworthy, Philip C.
2012
Multiscale analysis of pattern formation via intercellular signalling. Zbl 1214.92006
O’Dea, R. D.; King, J. R.
2011
Exponential asymptotics of homoclinic snaking. Zbl 1241.35017
Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.
2011
Contracting bubbles in Hele-Shaw cells with a power-law fluid. Zbl 1215.35174
McCue, Scott W.; King, John R.
2011
Very slow grow-up of solutions of a semi-linear parabolic equation. Zbl 1221.35064
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2011
Mathematical modelling of the sporulation-initiation network in bacillus subtilis revealing the dual role of the putative quorum-sensing signal molecule PhrA. Zbl 1209.92013
Jabbari, Sara; Heap, John T.; King, John R.
2011
The influence of cytokinin-auxin cross-regulation on cell-fate determination in Arabidopsis thaliana root development. Zbl 1397.92294
Muraro, Daniele; Byrne, Helen; King, John; Voß, Ute; Kieber, Joseph; Bennett, Malcolm
2011
The effect of mass transfer on steady two-dimensional rimming flow. Zbl 1254.76065
Noakes, Caroline J.; King, John R.; Riley, David S.
2011
Continuum approximations of individual-based models for epithelial monolayers. Zbl 1184.92011
Fozard, J. A.; Byrne, H. M.; Jensen, O. E.; King, J. R.
2010
Mathematical modelling of the agroperon in staphylococcus aureus. Zbl 1202.92041
Jabbari, Sara; King, John R.; Koerber, Adrian J.; Williams, Paul
2010
A multiple timescale analysis of a mathematical model of the Wnt/$$\beta$$-catenin signalling pathway. Zbl 1311.92094
Mirams, Gary R.; Byrne, Helen M.; King, John R.
2010
Mathematical modelling of the $$Aux/IAA$$ negative feedback loop. Zbl 1198.92005
Middleton, A. M.; King, J. R.; Bennett, M. J.; Owen, M. R.
2010
Similarity: Generalizations, applications and open problems. Zbl 1188.00015
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.
2010
Modelling of the activation of G-protein coupled receptors: drug free constitutive receptor activity. Zbl 1311.92097
Woodroffe, P. J.; Bridge, L. J.; King, J. R.; Chen, C. Y.; Hill, S. J.
2010
A mathematical investigation of the effects of inhibitor therapy on three putative phosphorylation cascades governing the two-component system of the agr operon. Zbl 1193.92033
Jabbari, Sara; King, John R.; Williams, Paul
2010
Front propagation in a heterogeneous Fisher equation: the homogeneous case is non-generic. Zbl 1228.35121
Cuesta, C. M.; King, J. R.
2010
Asymptotic analysis of extinction behaviour in fast nonlinear diffusion. Zbl 1188.76253
King, J. R.
2010
Mathematical modelling of signalling in a two-ligand G-protein coupled receptor system: agonist-antagonist competition. Zbl 1183.92026
Bridge, L. J.; King, J. R.; Hill, S. J.; Owen, M. R.
2010
Vanishing beyond all orders: Stokes lines in a water-wave model equation. Zbl 1198.34074
van den Berg, Jan Bouwe; King, John R.
2010
Modelling the activation of G-protein coupled receptors by a single drug. Zbl 1187.92043
Woodroffe, P. J.; Bridge, L. J.; King, J. R.; Hill, S. J.
2009
A bistable genetic switch which does not require high co-operativity at the promoter: a two-timescale model for the PU.1-GATA-1 interaction. Zbl 1163.92314
Bokes, Pavol; King, John R.; Loose, Matthew
2009
Bistability in a model of mesoderm and anterior mesendoderm specification in Xenopus laevis. Zbl 1402.92055
Middleton, Alistair M.; King, John R.; Loose, Matt
2009
Quadrature domains and $$p$$-Laplacian growth. Zbl 1179.35351
King, John R.; Mccue, Scott W.
2009
Linear stability analysis of a sharp-interface model for dewetting thin films. Zbl 1160.76017
King, J. R.; Münch, A.; Wagner, B. A.
2009
Mathematical modelling of tissue-engineered angiogenesis. Zbl 1175.92028
Lemon, Greg; Howard, Daniel; Tomlinson, Matthew J.; Buttery, Lee D.; Rose, Felicity R. A. J.; Waters, Sarah L.; King, John R.
2009
Interactions between a uniformly proliferating tumour and its surroundings: stability analysis for variable material properties. Zbl 1213.74112
Franks, S. J.; King, J. R.
2009
Linear behaviour of solutions of a superlinear heat equation. Zbl 1263.35137
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2008
Population-scale modelling of cellular chemotaxis and aggregation. Zbl 1145.82022
Fozard, J. A.; King, J. R.
2008
Unstable sixth-order thin film equation. I: Blow-up similarity solutions. Zbl 1173.35562
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Source-type solutions of the fourth-order unstable thin film equation. Zbl 1156.35387
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Unstable sixth-order thin film equation. II: Global similarity patterns. Zbl 1173.35530
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Blow-up similarity solutions of the fourth-order unstable thin film equation. Zbl 1221.35296
Evans, J. D.; Galaktionov, V. A.; King, J. R.
2007
Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosity. Zbl 1118.92024
Lemon, G.; King, J. R.
2007
Small- and waiting-time behavior of the thin-film equation. Zbl 1178.35388
Blowey, James F.; King, John R.; Langdon, Stephen
2007
Mathematical analysis of a model describing the invasion of bacteria in burn wounds. Zbl 1117.35036
Hilhorst, D.; King, J. R.; Röger, M.
2007
Why is a shock not a caustic? The higher-order Stokes phenomenon and smoothed shock formation. Zbl 1135.34044
Chapman, S. J.; Howls, C. J.; King, J. R.; Olde Daalhuis, A. B.
2007
Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Zbl 1170.35456
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2007
Modelling scaffold occupation by a growing, nutrient-rich tissue. Zbl 1135.92010
Wilson, Duncan J.; King, John R.; Byrne, Helen M.
2007
Time-dependent modelling and asymptotic analysis of electrochemical cells. Zbl 1125.92066
Richardson, G.; King, J. R.
2007
Mathematical modelling of nutrient-limited tissue growth. Zbl 1119.35122
King, J. R.; Franks, S. J.
2007
Travelling-wave behaviour in a multiphase model of a population of cells in an artificial scaffold. Zbl 1125.92030
Lemon, G.; King, J. R.
2007
Travelling-wave analysis of a model describing tissue degradation by bacteria. Zbl 1130.92031
Hilhorst, D.; King, J. R.; Röger, M.
2007
Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. Zbl 1110.92016
Lemon, Greg; King, John R.; Byrne, Helen M.; Jensen, Oliver E.; Shakesheff, Kevin M.
2006
Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2006
Modelling the response of spatially structured tumours to chemotherapy: drug kinetics. Zbl 1130.92033
Norris, E. S.; King, J. R.; Byrne, H. M.
2006
A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm. Zbl 1101.92020
Anguige, K.; King, J. R.; Ward, J. P.
2006
On the development of rational approximations incorporating inertial effects in coating and rimming flows: a multiple-scales approach. Zbl 1090.76008
Noakes, C. J.; King, J. R.; Riley, D. S.
2006
Lie symmetries and conservation laws of nonlinear multidimensional reaction-diffusion systems with variable diffusivities. Zbl 1122.35053
Cherniha, Roman; King, John R.
2006
Linear stability of a ridge. Zbl 1124.76015
King, J. R.; Münch, A.; Wagner, B.
2006
Small- and waiting-time behaviour of a Darcy flow model with a dynamic pressure saturation relation. Zbl 1115.35076
Cuesta, C. M.; King, J. R.
2006
Ray methods for free boundary problems. Zbl 1117.35083
Addison, J. A.; Howison, S. D.; King, J. R.
2006
Intermediate-asymptotic structure of a dewetting rim with strong slip. Zbl 1109.76010
Evans, P. L.; King, J. R.; Münch, A.
2006
Nonlinear reaction-diffusion systems with variable diffusivities: Lie symmetries, ansätze and exact solutions. Zbl 1073.35115
Cherniha, Roman; King, John R.
2005
Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population. Zbl 1091.92036
Anguige, K.; King, J. R.; Ward, J. P.
2005
Regularization by kinetic undercooling of blow-up in the ill-posed Stefan problem. Zbl 1099.35178
King, J. R.; Evans, J. D.
2005
The extinction problem for three-dimensional inward solidification. Zbl 1092.80007
McCue, Scott W.; King, John R.; Riley, David S.
2005
Thin-film modelling of poroviscous free surface flows. Zbl 1112.76021
King, J. R.; Oliver, J. M.
2005
...and 115 more Documents
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#### Cited by 1,631 Authors

 91 King, John Robert 30 Byrne, Helen Mary 16 Galaktionov, Victor Aleksandrovich 15 Cherniha, Roman M. 15 Vazquez, Juan Luis 15 Whiteley, Jonathan P. 13 Qu, Changzheng 12 Liu, Chein-Shan 12 Waters, Sarah Louise 12 Winkler, Michael 11 Fila, Marek 11 Lustri, Christopher J. 11 McCue, Scott William 11 Mo, Jiaqi 11 Taranets, Roman M. 10 Chapman, Stephen Jonathan 10 Friedman, Avner 10 Maini, Philip Kumar 10 O’Dea, Reuben D. 10 Tao, Youshan 10 Yanagida, Eiji 9 Abdulla, Ugur G. 9 Semenov, Edward Ivanovich 9 Sophocleous, Christodoulos 8 Del Pino, Manuel A. 8 Guo, Qian 8 Jabbari, Sara 8 Momoniat, Ebrahim 8 Please, Colin P. 8 Preziosi, Luigi 8 Serov, Mykola I. 8 Witelski, Thomas P. 7 Chugunova, Marina A. 7 Daskalopoulos, Panagiota 7 Ji, Lina 7 Lowengrub, John Samuel 7 McDonald, N. Robb 7 Münch, Andreas 7 Oliver, James M. 7 Simpson, Matthew J. 7 Yin, Jingxue 6 Álvarez-Caudevilla, Pablo 6 Bridge, Lloyd J. 6 Cristini, Vittorio 6 Iagar, Razvan Gabriel 6 Lin, Wantao 6 Lorenzi, Tommaso 6 Perthame, Benoît 6 Raphael, Pierre 6 Sánchez, Ariel 6 Ward, John Paul 6 Zhang, Juan 6 Zhang, Zhonghua 5 Bennett, Malcolm J. 5 Bokes, Pavol 5 Chaplain, Mark A. J. 5 Cuesta Romero, Carlota Maria 5 Cui, Shangbin 5 Cummings, Linda J. 5 Dalwadi, Mohit P. 5 Davydovych, Vasyl’ 5 Drasdo, Dirk 5 Evans, Jonathan David 5 Hilhorst, Danielle 5 Hill, James Murray 5 Hsu, Shu-Yu 5 Hu, Bei 5 Hubbard, Matthew E. 5 Kosov, Aleksandr Arkad’evich 5 Loose, Matthew 5 Okrasiński, Wojciech 5 Owen, Markus Roger 5 Quirós Gracián, Fernando 5 Savina, Tatiana V. 5 Sesum, Natasa 5 Shen, Shoufeng 5 Tarzia, Domingo Alberto 5 Trinh, Philippe H. 5 Vella, Dominic 5 Wei, Juncheng 5 Wu, Junde 5 Xu, Shihe 5 Zhang, Zhengce 5 Zhou, Fujun 4 Aihara, Kazuyuki 4 Ambrosi, Davide 4 Baker, Ruth Elizabeth 4 Collis, Joe 4 Duffy, Brian Reginald 4 Eberl, Hermann J. 4 Fletcher, Alexander G. 4 Frieboes, Hermann B. 4 Gandolfi, Alberto 4 Giacomelli, Lorenzo 4 Goriely, Alain 4 Green, J. Edward F. 4 Mu, Chunlai 4 Myers, Timothy G. 4 Ockendon, John R. 4 Poignard, Clair ...and 1,531 more Authors
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#### Cited in 202 Serials

 61 Journal of Mathematical Biology 59 Journal of Theoretical Biology 45 Journal of Fluid Mechanics 43 Bulletin of Mathematical Biology 42 Journal of Mathematical Analysis and Applications 40 Journal of Engineering Mathematics 39 European Journal of Applied Mathematics 38 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 32 Mathematical Biosciences 27 Journal of Differential Equations 22 Applied Mathematics and Computation 19 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 18 SIAM Journal on Applied Mathematics 18 Physics of Fluids 16 Physica D 14 Mathematical and Computer Modelling 13 Communications in Nonlinear Science and Numerical Simulation 12 Journal of Computational and Applied Mathematics 12 Studies in Applied Mathematics 12 Applied Mathematics Letters 11 Archive for Rational Mechanics and Analysis 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Discrete and Continuous Dynamical Systems 10 Nonlinear Analysis. Real World Applications 9 Journal of Mathematical Physics 9 NoDEA. Nonlinear Differential Equations and Applications 8 Mathematical Methods in the Applied Sciences 8 Nonlinearity 8 Communications in Partial Differential Equations 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Applied Mathematical Modelling 7 Applied Mathematics. Series B (English Edition) 7 Abstract and Applied Analysis 6 Computers & Mathematics with Applications 6 Journal of Mathematical Sciences (New York) 6 Discrete and Continuous Dynamical Systems. Series B 6 SIAM Journal on Applied Dynamical Systems 6 Boundary Value Problems 6 Symmetry 5 Applicable Analysis 5 Fluid Dynamics 5 International Journal of Engineering Science 5 Mathematics and Computers in Simulation 5 SIAM Journal on Mathematical Analysis 5 Journal of Physics A: Mathematical and Theoretical 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Acta Mechanica 4 Computers and Fluids 4 Physica A 4 Rocky Mountain Journal of Mathematics 4 Wave Motion 4 Journal of Functional Analysis 4 Journal für die Reine und Angewandte Mathematik 4 Mathematische Annalen 4 Quarterly of Applied Mathematics 4 Siberian Mathematical Journal 4 Transactions of the American Mathematical Society 4 Journal of Scientific Computing 4 Journal of Nonlinear Science 4 Calculus of Variations and Partial Differential Equations 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Interfaces and Free Boundaries 4 The ANZIAM Journal 4 Mathematical Biosciences and Engineering 4 Computational & Mathematical Methods in Medicine 4 International Journal of Differential Equations 3 Bulletin of the Australian Mathematical Society 3 Communications on Pure and Applied Mathematics 3 Journal of Computational Physics 3 Journal of the Mechanics and Physics of Solids 3 Advances in Mathematics 3 SIAM Journal on Numerical Analysis 3 Applied Numerical Mathematics 3 Acta Mathematicae Applicatae Sinica. English Series 3 Science in China. Series A 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Dynamics and Differential Equations 3 Mathematical Problems in Engineering 3 European Journal of Mechanics. B. Fluids 3 Multiscale Modeling & Simulation 3 Discrete and Continuous Dynamical Systems. Series S 3 Nonlinear Analysis. Theory, Methods & Applications 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Fluids 2 Israel Journal of Mathematics 2 Journal of Statistical Physics 2 Reports on Mathematical Physics 2 Ukrainian Mathematical Journal 2 Mathematics of Computation 2 Glasgow Mathematical Journal 2 Inventiones Mathematicae 2 Manuscripta Mathematica 2 The Journal of Geometric Analysis 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Cybernetics and Systems Analysis 2 Computational and Applied Mathematics 2 Doklady Mathematics 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Nonlinear Mathematical Physics ...and 102 more Serials
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#### Cited in 41 Fields

 658 Partial differential equations (35-XX) 380 Biology and other natural sciences (92-XX) 302 Fluid mechanics (76-XX) 103 Numerical analysis (65-XX) 75 Ordinary differential equations (34-XX) 56 Dynamical systems and ergodic theory (37-XX) 51 Mechanics of deformable solids (74-XX) 44 Classical thermodynamics, heat transfer (80-XX) 29 Global analysis, analysis on manifolds (58-XX) 29 Statistical mechanics, structure of matter (82-XX) 25 Differential geometry (53-XX) 22 Probability theory and stochastic processes (60-XX) 17 Optics, electromagnetic theory (78-XX) 16 Systems theory; control (93-XX) 10 Integral equations (45-XX) 9 Functions of a complex variable (30-XX) 9 Operator theory (47-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Potential theory (31-XX) 7 Computer science (68-XX) 6 Special functions (33-XX) 6 Statistics (62-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Difference and functional equations (39-XX) 5 Approximations and expansions (41-XX) 4 Mechanics of particles and systems (70-XX) 3 Functional analysis (46-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Quantum theory (81-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX)