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## Billingham, John

Compute Distance To:
 Author ID: billingham.john Published as: Billingham, J.; Billingham, John
 Documents Indexed: 61 Publications since 1991, including 3 Books
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#### Co-Authors

 14 single-authored 19 King, Andrew C. 14 Needham, David John 4 Jensen, Oliver E. 3 Preece, S. J. 2 Gallagher, Meurig T. 2 Thompson, Alice B. 2 Xu, Feng 1 Adamson, F. 1 Axinte, D. A. 1 Bailey, Paul B. 1 Bain, Oliver 1 Benilov, Eugene S. 1 Bradshaw, J. T. 1 Chamberlain, Peter G. 1 Copcutt, R. C. 1 Everitt, William Norrie 1 Falle, Sam A. E. G. 1 Ferguson, J. W. J. 1 Francis, D. T. I. 1 Harrisson, A. M. 1 Houston, Paul 1 Kong, Qingkai 1 Korsukova, E. 1 Lowndes, Ian S. 1 Lozano Torrubia, P. 1 Marchbanks, R. J. 1 Mercer, Geoffry Norman 1 Munro, R. J. 1 Otto, S. R. 1 Popple, D. F. 1 Rasheed, S. M. 1 Salhan, Anjulika 1 Schulkes, R. M. S. M. 1 Sharpe, Gary J. 1 Tew, Richard H. 1 Tuck, Ernest O. 1 Williams, Peter M. 1 Woollard, H. F. 1 Wu, Hongyou 1 Zettl, Anton
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#### Serials

 16 Journal of Fluid Mechanics 7 IMA Journal of Applied Mathematics 7 Journal of Engineering Mathematics 3 Quarterly Journal of Mechanics and Applied Mathematics 3 SIAM Journal on Applied Mathematics 3 Philosophical Transactions of the Royal Society of London. Series A 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Dynamics and Stability of Systems 2 Combustion Theory and Modelling 1 Nonlinearity 1 Quarterly of Applied Mathematics 1 European Journal of Applied Mathematics 1 Journal of Non-Newtonian Fluid Mechanics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Journal of Mathematical Chemistry 1 Mathematical Medicine and Biology 1 Mathematical Modelling of Natural Phenomena 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Cambridge Texts in Applied Mathematics
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#### Fields

 41 Fluid mechanics (76-XX) 13 Biology and other natural sciences (92-XX) 11 Partial differential equations (35-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Ordinary differential equations (34-XX) 6 Mechanics of deformable solids (74-XX) 4 Geophysics (86-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

41 Publications have been cited 306 times in 250 Documents Cited by Year
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I: Permanent form travelling waves. Zbl 0739.35033
Billingham, J.; Needham, D. J.
1991
Wave motion. Zbl 0973.76001
Billingham, John; King, Andrew C.
2000
Dynamics of a strongly nonlocal reaction-diffusion population model. Zbl 1050.35038
Billingham, John
2004
A note on the properties of a family of travelling-wave solutions arising in cubic autocatalysis. Zbl 0737.35031
Billingham, J.; Needham, D. J.
1991
Differential equations. Linear, nonlinear, ordinary, partial. Zbl 1034.34001
King, A. C.; Billingham, J.; Otto, S. R.
2003
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. II: An initial-value problem with an immobilized or nearly immobilized autocatalyst. Zbl 0762.35048
Billingham, J.; Needham, D. J.
1991
Uniform asymptotic expansions for the Barnes double gamma function. Zbl 0926.33001
Billingham, J.; King, A. C.
1997
Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis. Zbl 1149.76621
Clarke, R. J.; Jensen, O. E.; Billingham, J.; Williams, P. M.
2006
The initial development of a jet caused by fluid, body and free surface interaction. III: An inclined accelerating plate. Zbl 1153.76019
Needham, D. J.; Chamberlain, P. G.; Billingham, J.
2008
The initial development of a jet caused by fluid, body and free-surface interaction. II: An impulsively moved plate. Zbl 1116.76013
Needham, D. J.; Billingham, J.; King, A. C.
2007
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. III: Large time development in quadratic autocatalysis. Zbl 0787.35042
Billingham, J.; Needham, D. J.
1992
Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms. Zbl 0954.34041
Billingham, John
2000
On a model for the motion of a contact line on a smooth solid surface. Zbl 1201.76060
Billingham, J.
2006
The effect of heat loss on the propagation of strongly exothermic combustion waves. Zbl 1023.76054
Billingham, J.; Mercer, G. N.
2001
Nonlinear sloshing in zero gravity. Zbl 1043.76019
Billingham, John
2002
An asymptotic theory for the propagation of a surface-catalysed flame in a tube. Zbl 1097.76072
Adamson, F.; Billingham, J.; King, A. C.; Kendall, K.
2006
Gravity-driven thin-film flow using a new contact line model. Zbl 1139.76009
Billingham, J.
2008
A multi-scale model for solute transport in a wavy-walled channel. Zbl 1160.76048
Woollard, H. F.; Billingham, J.; Jensen, O. E.; Lian, G.
2009
Drops climbing uphill on an oscillating substrate. Zbl 1241.76066
Benilov, E. S.; Billingham, J.
2011
Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux. Zbl 1287.76253
Xu, Feng; Billingham, John; Jensen, Oliver E.
2013
Surface tension-driven flow in a slender wedge. Zbl 1127.76010
Billingham, J.
2006
Resonance-driven oscillations in a flexible-channel flow with fixed upstream flux and a long downstream rigid segment. Zbl 1309.76236
Xu, Feng; Billingham, John; Jensen, Oliver E.
2014
The interaction of a moving fluid/fluid interface with a flat plate. Zbl 0888.76084
Billingham, J.; King, A. C.
1995
On the initial stages of cement hydration. Zbl 1017.76088
Preece, S. J.; Billingham, J.; King, A. C.
2001
Laminar, unidirectional flow of a thixotropic fluid in a circular pipe. Zbl 0781.76003
Billingham, J.; Ferguson, J. W. J.
1993
Surface-tension-driven flow in fat fluid wedges and cones. Zbl 0967.76031
Billingham, John
1999
Chemical clock reactions: The effect of precursor consumption. Zbl 0991.92041
Preece, S. J.; Billingham, J.; King, A. C.
1999
Steady-state solutions for strongly exothermic ignition in symmetric geometries. Zbl 1005.80007
Billingham, John
2000
Flow and reaction in solid oxide fuel cells. Zbl 0955.76096
Cooper, R. J.; Billingham, J.; King, A. C.
2000
Mathematical modelling of chemical clock reactions. II: A class of autocatalytic clock reaction schemes. Zbl 0778.92029
Billingham, J.; Needham, D. J.
1993
A multiphase model for the early stages of the hydration of retarded oilwell cement. Zbl 1124.76321
Billingham, J.; Francis, D. T. I.; King, A. C.; Harrisson, A. M.
2005
The effect of a retarder on the early stages of the hydration of tricalcium silicate. Zbl 1029.92029
Salhan, A.; Billingham, J.; King, A. C.
2003
On some eigenvalue problems in fuel-cell dynamics. Zbl 1056.34091
Bailey, P. B.; Billingham, J.; Cooper, R. J.; Everitt, W. N.; King, A. C.; Kong, Q.; Wu, H.; Zettl, A.
2003
The initial surface tension-driven flow of a wedge of viscous fluid. Zbl 1131.76023
Billingham, J.
2005
Mathematical modelling of chemical clock reactions. I: Induction, inhibition and the iodate-arsenous-acid reaction. Zbl 0778.92028
Billingham, J.; Needham, D. J.
1992
Stochastic simplified modelling of abrasive waterjet footprints. Zbl 1371.76023
Lozano Torrubia, P.; Billingham, J.; Axinte, D. A.
2016
Surface-tension-driven flow outside a slender wedge with an application to the inviscid coalescence of drops. Zbl 1100.76015
Billingham, J.; King, A. C.
2005
A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes’ theory. Zbl 1186.76625
Needham, D. J.; Billingham, J.
2009
The evolution of travelling leaves from chemical-clock reactions. Zbl 0978.92036
Preece, S. J.; Billingham, J.; King, A. C.
2001
Inviscid coalescence in the presence of a surrounding fluid. Zbl 1316.76029
Thompson, Alice B.; Billingham, John
2012
Thick drops climbing uphill on an oscillating substrate. Zbl 1419.76193
2018
Thick drops climbing uphill on an oscillating substrate. Zbl 1419.76193
2018
Stochastic simplified modelling of abrasive waterjet footprints. Zbl 1371.76023
Lozano Torrubia, P.; Billingham, J.; Axinte, D. A.
2016
Resonance-driven oscillations in a flexible-channel flow with fixed upstream flux and a long downstream rigid segment. Zbl 1309.76236
Xu, Feng; Billingham, John; Jensen, Oliver E.
2014
Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux. Zbl 1287.76253
Xu, Feng; Billingham, John; Jensen, Oliver E.
2013
Inviscid coalescence in the presence of a surrounding fluid. Zbl 1316.76029
Thompson, Alice B.; Billingham, John
2012
Drops climbing uphill on an oscillating substrate. Zbl 1241.76066
Benilov, E. S.; Billingham, J.
2011
A multi-scale model for solute transport in a wavy-walled channel. Zbl 1160.76048
Woollard, H. F.; Billingham, J.; Jensen, O. E.; Lian, G.
2009
A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes’ theory. Zbl 1186.76625
Needham, D. J.; Billingham, J.
2009
The initial development of a jet caused by fluid, body and free surface interaction. III: An inclined accelerating plate. Zbl 1153.76019
Needham, D. J.; Chamberlain, P. G.; Billingham, J.
2008
Gravity-driven thin-film flow using a new contact line model. Zbl 1139.76009
Billingham, J.
2008
The initial development of a jet caused by fluid, body and free-surface interaction. II: An impulsively moved plate. Zbl 1116.76013
Needham, D. J.; Billingham, J.; King, A. C.
2007
Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis. Zbl 1149.76621
Clarke, R. J.; Jensen, O. E.; Billingham, J.; Williams, P. M.
2006
On a model for the motion of a contact line on a smooth solid surface. Zbl 1201.76060
Billingham, J.
2006
An asymptotic theory for the propagation of a surface-catalysed flame in a tube. Zbl 1097.76072
Adamson, F.; Billingham, J.; King, A. C.; Kendall, K.
2006
Surface tension-driven flow in a slender wedge. Zbl 1127.76010
Billingham, J.
2006
A multiphase model for the early stages of the hydration of retarded oilwell cement. Zbl 1124.76321
Billingham, J.; Francis, D. T. I.; King, A. C.; Harrisson, A. M.
2005
The initial surface tension-driven flow of a wedge of viscous fluid. Zbl 1131.76023
Billingham, J.
2005
Surface-tension-driven flow outside a slender wedge with an application to the inviscid coalescence of drops. Zbl 1100.76015
Billingham, J.; King, A. C.
2005
Dynamics of a strongly nonlocal reaction-diffusion population model. Zbl 1050.35038
Billingham, John
2004
Differential equations. Linear, nonlinear, ordinary, partial. Zbl 1034.34001
King, A. C.; Billingham, J.; Otto, S. R.
2003
The effect of a retarder on the early stages of the hydration of tricalcium silicate. Zbl 1029.92029
Salhan, A.; Billingham, J.; King, A. C.
2003
On some eigenvalue problems in fuel-cell dynamics. Zbl 1056.34091
Bailey, P. B.; Billingham, J.; Cooper, R. J.; Everitt, W. N.; King, A. C.; Kong, Q.; Wu, H.; Zettl, A.
2003
Nonlinear sloshing in zero gravity. Zbl 1043.76019
Billingham, John
2002
The effect of heat loss on the propagation of strongly exothermic combustion waves. Zbl 1023.76054
Billingham, J.; Mercer, G. N.
2001
On the initial stages of cement hydration. Zbl 1017.76088
Preece, S. J.; Billingham, J.; King, A. C.
2001
The evolution of travelling leaves from chemical-clock reactions. Zbl 0978.92036
Preece, S. J.; Billingham, J.; King, A. C.
2001
Wave motion. Zbl 0973.76001
Billingham, John; King, Andrew C.
2000
Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms. Zbl 0954.34041
Billingham, John
2000
Steady-state solutions for strongly exothermic ignition in symmetric geometries. Zbl 1005.80007
Billingham, John
2000
Flow and reaction in solid oxide fuel cells. Zbl 0955.76096
Cooper, R. J.; Billingham, J.; King, A. C.
2000
Surface-tension-driven flow in fat fluid wedges and cones. Zbl 0967.76031
Billingham, John
1999
Chemical clock reactions: The effect of precursor consumption. Zbl 0991.92041
Preece, S. J.; Billingham, J.; King, A. C.
1999
Uniform asymptotic expansions for the Barnes double gamma function. Zbl 0926.33001
Billingham, J.; King, A. C.
1997
The interaction of a moving fluid/fluid interface with a flat plate. Zbl 0888.76084
Billingham, J.; King, A. C.
1995
Laminar, unidirectional flow of a thixotropic fluid in a circular pipe. Zbl 0781.76003
Billingham, J.; Ferguson, J. W. J.
1993
Mathematical modelling of chemical clock reactions. II: A class of autocatalytic clock reaction schemes. Zbl 0778.92029
Billingham, J.; Needham, D. J.
1993
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. III: Large time development in quadratic autocatalysis. Zbl 0787.35042
Billingham, J.; Needham, D. J.
1992
Mathematical modelling of chemical clock reactions. I: Induction, inhibition and the iodate-arsenous-acid reaction. Zbl 0778.92028
Billingham, J.; Needham, D. J.
1992
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I: Permanent form travelling waves. Zbl 0739.35033
Billingham, J.; Needham, D. J.
1991
A note on the properties of a family of travelling-wave solutions arising in cubic autocatalysis. Zbl 0737.35031
Billingham, J.; Needham, D. J.
1991
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. II: An initial-value problem with an immobilized or nearly immobilized autocatalyst. Zbl 0762.35048
Billingham, J.; Needham, D. J.
1991
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#### Cited by 417 Authors

 12 Billingham, John 9 Merkin, John H. 9 Needham, David John 6 Qi, Yuanwei 6 Wang, Zhi Cheng 5 Li, Wan-Tong 5 López, José Luis 4 Gaffney, Eamonn A. 4 Korobkin, Alexander A. 4 Lister, John R. 4 Popović, Nikola 4 Ruan, Shigui 4 Saad, Khaled Mohammed 3 Bai, Chen-Yuan 3 Blake, John Robert 3 Blyth, Mark G. 3 Chen, Shanshan 3 Chen, Xinfu 3 Choi, Junesang 3 Ferreira, Chelo 3 Hamel, François 3 Kaper, Tasso J. 3 King, Andrew C. 3 Liu, Gui Rong 3 Liu, Zuhan 3 Mansour, Mahmoud Bakheet A. 3 Pérez Sinusía, Ester 3 Razani, Abdolrahman 3 Smith, David J. 3 Srivastava, Hari Mohan 3 Tsai, Je-Chiang 3 Waters, Sarah Louise 3 Wu, Ziniu 3 Zhou, Ling 2 Abrahams, I. David 2 Balasuriya, Sanjeeva 2 Bennetts, Luke G. 2 Binder, Benjamin James 2 Caraballo Garrido, Tomás 2 Christodoulou, Dimitris M. 2 Cooker, Mark J. 2 Ding, Hang 2 Fried, Eliot 2 Gallagher, Meurig T. 2 Ghazaryan, Anna 2 Graham-Eagle, James 2 Green, J. Edward F. 2 Han, Bang-Sheng 2 Herrera-Cobos, Marta 2 Hosono, Yuzo 2 Jabbour, Michel E. 2 Jia, Yunfeng 2 Kalliadasis, Serafim 2 Katatbeh, Qutaibeh Deeb 2 Kudryashov, Nikolaĭ Alekseevich 2 Kuznetsov, Alexey 2 Malham, Simon J. A. 2 Marín-Rubio, Pedro 2 Mercer, Geoffry Norman 2 Munro, James P. 2 Nicholls, David P. 2 Părău, Emilian I. 2 Pažanin, Igor 2 Ryzhik, Lenya 2 Sadiq, Muhammad Adil 2 Semenov, Yuriy A. 2 Shi, Junping 2 Simon, Thomas 2 Skene, David M. 2 Spelt, Peter D. M. 2 Stewart, Peter S. 2 Thoroddsen, Sigurdur T. 2 Tyvand, Peder A. 2 Ungarish, Marius 2 Vella, Dominic 2 Whiteley, Jonathan P. 2 Wu, Yaping 2 Yu, Jian-She 2 Zhao, Yaling 1 Abdelati, Riadh 1 Afkhami, Shahriar 1 Agnon, Yehuda 1 Ai, Shangbing 1 Akrish, Gal 1 Aksoy, Serkan 1 Al-Sharif, Eman Hussain Faissal 1 Alkumru, Ali 1 Ancey, Christophe 1 Andriopoulos, Kostis 1 Anthony, Christopher R. 1 Antkowiak, Arnaud 1 Aparicio, Nairo D. 1 Auroux, Didier 1 Baker, Greg R. 1 Băleanu, Dumitru I. 1 Balmforth, Neil J. 1 Band, Leah R. 1 Barta, Efrath 1 Basak, Sudipta 1 Basaran, Osman A. ...and 317 more Authors
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#### Cited in 87 Serials

 41 Journal of Fluid Mechanics 16 Journal of Differential Equations 14 Journal of Engineering Mathematics 9 Journal of Mathematical Analysis and Applications 6 Journal of Computational Physics 6 Physics of Fluids 6 Journal of Mathematical Chemistry 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 6 Discrete and Continuous Dynamical Systems. Series B 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Applied Mathematics and Computation 5 Applied Mathematics Letters 4 Archive for Rational Mechanics and Analysis 4 Quarterly of Applied Mathematics 4 Physica D 4 European Journal of Mechanics. B. Fluids 4 Nonlinear Analysis. Real World Applications 3 Bulletin of Mathematical Biology 3 Mathematics and Computers in Simulation 3 Acta Applicandae Mathematicae 3 Mathematical and Computer Modelling 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Communications in Nonlinear Science and Numerical Simulation 3 Combustion Theory and Modelling 3 Journal of Theoretical Biology 2 International Journal for Numerical Methods in Fluids 2 Journal of Mathematical Biology 2 Journal of Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Wave Motion 2 Mathematics of Computation 2 Reviews in Mathematical Physics 2 Chaos, Solitons and Fractals 2 Japan Journal of Industrial and Applied Mathematics 2 Applied Mathematical Modelling 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Engineering Analysis with Boundary Elements 2 Discrete and Continuous Dynamical Systems 2 The ANZIAM Journal 2 Communications on Pure and Applied Analysis 2 Advances in Difference Equations 1 International Journal of Modern Physics B 1 Acta Mechanica 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Physica A 1 The Annals of Probability 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 BIT 1 Journal of Approximation Theory 1 Journal of Number Theory 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Theoretical Population Biology 1 Transactions of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Dynamics and Stability of Systems 1 Forum Mathematicum 1 Journal of Integral Equations and Applications 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Non-Newtonian Fluid Mechanics 1 SIAM Journal on Applied Mathematics 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Computational and Applied Mathematics 1 Journal of the Egyptian Mathematical Society 1 Electronic Journal of Probability 1 European Journal of Control 1 Differential Equations and Dynamical Systems 1 Journal of Inequalities and Applications 1 Chaos 1 Journal of Nonlinear Mathematical Physics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Sādhanā 1 Computational Methods and Function Theory 1 Inverse Problems in Science and Engineering 1 Discrete and Continuous Dynamical Systems. Series S 1 Science China. Mathematics 1 Afrika Matematika 1 International Journal of Engineering Mathematics
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#### Cited in 27 Fields

 106 Partial differential equations (35-XX) 99 Fluid mechanics (76-XX) 63 Biology and other natural sciences (92-XX) 39 Ordinary differential equations (34-XX) 27 Numerical analysis (65-XX) 22 Classical thermodynamics, heat transfer (80-XX) 18 Mechanics of deformable solids (74-XX) 11 Dynamical systems and ergodic theory (37-XX) 8 Geophysics (86-XX) 7 Special functions (33-XX) 6 Probability theory and stochastic processes (60-XX) 5 Approximations and expansions (41-XX) 5 Integral equations (45-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Number theory (11-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Statistics (62-XX)