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Ward, Michael J.

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 Author ID: ward.michael-j Published as: Ward, Michael J.; Ward, M. J.; Ward, Michael; Ward, M. Homepage: https://secure.math.ubc.ca/~ward/ External Links: MGP
 Documents Indexed: 151 Publications since 1989
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Co-Authors

 15 single-authored 26 Wei, Juncheng 21 Kolokolnikov, Theodore 9 Reyna, Luis Guillermo M. 9 Tzou, Justin C. 8 Iron, David 6 Lindsay, Alan E. 5 Keller, Joseph Bishop 5 Titcombe, Michèle S. 4 Gou, Jia 4 Kropinski, Mary Catherine A. 4 Nec, Yana 4 Odeh, F. M. 4 Paquin-Lefebvre, Frédéric 4 Straube, Ronny 4 Sun, Xiaodi 3 Breña-Medina, Víctor F. 3 Cheviakov, Alexei F. 3 Coombs, Daniel 3 King, John Robert 3 Nagata, Wayne 3 Sun, Wentao 3 Tse, Wang Hung 2 Avitabile, Daniele 2 Champneys, Alan R. 2 Chen, Wan 2 Edelstein-Keshet, Leah 2 Fadai, Nabil T. 2 Gomez, Daniel 2 Howison, Sam D. 2 Iyaniwura, Sarafa A. 2 Lacey, Andrew A. 2 Li, Yuexian 2 Moyles, Iain R. 2 O’Malley, Robert E. jun. 2 Rumsey, John R. 2 Small, Tim 2 Stafford, Douglas 2 Trinh, Philippe H. 2 Van de Velde, Eric F. 2 Wetton, Brian R. 2 Zmurchok, Cole 1 Audsley, Neil C. 1 Bernoff, Andrew J. 1 Bertozzi, Andrea Louise 1 Bluman, George W. 1 Brădean, Radu 1 Brauer, Fred 1 Bressloff, Paul C. 1 Brewster, M. Q. 1 Bridge, Lloyd J. 1 Broadbridge, Philip 1 Burger, Martin 1 Chiang, Wei-Yin 1 Cohen, Donald Sussman 1 Costello, Christopher J. 1 David, Jummy Funke 1 Delgado, M. I. 1 Earnshaw, Berton A. 1 Falcke, Martin 1 Gavaghan, David J. 1 Grierson, C. 1 Guo, Yujin 1 Henshaw, William D. 1 Hormozi, Sarah 1 Houston, Paul 1 Jamieson-Lane, Alastair 1 Johnson, Shane D. 1 Kang, Kyungkeun 1 Kurella, Venu 1 Laforgue, Jacques G. L. 1 Lai, Pik-Yin 1 Lee, June-Yub 1 Maini, Philip Kumar 1 McInerney, Darragh 1 Ou, Chunhua 1 Pan, Zhenguo 1 Peirce, Anthony P. 1 Randrianandrasana, Michel F. 1 Rottschäfer, Vivi 1 Rozada, Ignacio 1 Russell, Robert D. 1 Ruuth, Steven J. 1 Sleeman, Brian D. 1 Son, S. F. 1 Tang, Tao 1 Wei, Xueyong 1 Wolf, Sven Andreas 1 Xie, Shuangquan
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Serials

 24 SIAM Journal on Applied Mathematics 20 European Journal of Applied Mathematics 17 Studies in Applied Mathematics 14 SIAM Journal on Applied Dynamical Systems 7 Physica D 5 IMA Journal of Applied Mathematics 5 Methods and Applications of Analysis 4 Journal of Engineering Mathematics 4 Bulletin of Mathematical Biology 4 Journal of Nonlinear Science 4 Discrete and Continuous Dynamical Systems. Series B 4 Multiscale Modeling & Simulation 3 Nonlinearity 3 Applied Mathematics Letters 2 Journal of Environmental Economics and Management 2 Interfaces and Free Boundaries 2 Mathematical Modelling of Natural Phenomena 1 Communications on Pure and Applied Mathematics 1 International Journal of Mechanical Sciences 1 Journal of Statistical Physics 1 Canadian Mathematical Bulletin 1 International Journal for Numerical Methods in Engineering 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Applied Numerical Mathematics 1 Mathematical and Computer Modelling 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 The Canadian Applied Mathematics Quarterly 1 Mathematical Problems in Engineering 1 Natural Resource Modeling 1 Combustion Theory and Modelling 1 Analysis and Applications (Singapore) 1 Mathematical Biosciences and Engineering 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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Fields

 124 Partial differential equations (35-XX) 37 Biology and other natural sciences (92-XX) 22 Numerical analysis (65-XX) 15 Fluid mechanics (76-XX) 13 Ordinary differential equations (34-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Mechanics of deformable solids (74-XX) 9 Classical thermodynamics, heat transfer (80-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Probability theory and stochastic processes (60-XX) 3 Mechanics of particles and systems (70-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

Citations contained in zbMATH Open

124 Publications have been cited 1,554 times in 648 Documents Cited by Year
The stability of spike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 0983.35020
Iron, David; Ward, Michael J.; Wei, Juncheng
2001
Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties. Zbl 1103.35042
Guo, Yujin; Pan, Zhenguo; Ward, M. J.
2005
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Zbl 1030.35011
Ward, M. J.; Wei, J.
2003
Strong localized perturbations of eigenvalue problems. Zbl 0778.35081
Ward, Michael J.; Keller, Joseph B.
1993
Summing logarithmic expansions for singularly perturbed eigenvalue problems. Zbl 0778.35082
Ward, Michael J.; Henshaw, William D.; Keller, Joseph B.
1993
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The existence and stability of asymmetric spike patterns for the Schnakenberg model. Zbl 1152.35397
Ward, Michael J.; Wei, Juncheng
2002
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033
Chen, W.; Ward, M. J.
2011
The dynamics of multispike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 1019.35016
Iron, David; Ward, Michael J.
2002
An asymptotic analysis of the mean first passage time for narrow escape problems. II: The sphere. Zbl 1204.35030
Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny
2010
Hopf bifurction of spike solutions for the shadow Gierer-Meinhardt model. Zbl 1063.35030
Ward, M. J.; Wei, J.
2003
On the exponentially slow motion of a viscous shock. Zbl 0824.76042
Reyna, Luis G.; Ward, Michael J.
1995
Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability. Zbl 1010.35002
Ward, M. J.; Wei, J.
2002
The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404
Sun, Wentao; Ward, Michael J.; Russell, Robert
2005
Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Zbl 1090.35070
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J.
2005
The existence and stability of spike patterns in a chemotaxis model. Zbl 1073.35118
Sleeman, B. D.; Ward, Michael J.; Wei, J. C.
2005
Metastable bubble solutions for the Allen-Cahn equation with mass conservation. Zbl 0870.35011
Ward, Michael J.
1996
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps. Zbl 1219.35155
Cheviakov, A. F.; Ward, M. J.
2011
Diffusion on a sphere with localized traps: mean first passage time, eigenvalue asymptotics, and Fekete points. Zbl 1191.35032
Coombs, Daniel; Straube, Ronny; Ward, Michael
2009
The stability of localized spot patterns for the Brusselator on the sphere. Zbl 1302.35033
Rozada, Ignacio; Ruuth, Steven J.; Ward, M. J.
2014
Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. Zbl 1197.35021
Chen, Wan; Ward, Michael J.
2009
Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. Zbl 1364.35151
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T.
2015
A metastable spike solution for a nonlocal reaction-diffusion model. Zbl 0956.35011
Iron, David; Ward, Michael J.
2000
Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor: Part I: Fold point asymptotics. Zbl 1173.35625
Lindsay, A. E.; Ward, M. J.
2008
Dynamics and coarsening of interfaces for the viscous Cahn-Hilliard equation in one spatial dimension. Zbl 1136.74366
Sun, Xiaodi; Ward, Michael J.
2000
First passage statistics for the capture of a Brownian particle by a structured spherical target with multiple surface traps. Zbl 1372.35021
Lindsay, Alan E.; Bernoff, Andrew J.; Ward, Michael J.
2017
Eliminating indeterminacy in singularly perturbed boundary value problems with translation invariant potentials. Zbl 0767.65068
Ward, Michael J.
1992
Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. Zbl 1063.35024
Kolokolnikov, Theodore; Ward, Michael J.
2003
Metastability for a generalized Burgers equation with applications to propagating flame fronts. Zbl 0919.35122
Sun, X.; Ward, M. J.
1999
The dynamics of localized spot patterns for reaction-diffusion systems on the sphere. Zbl 1338.35248
Trinh, Philippe H.; Ward, Michael J.
2016
The stability and dynamics of a spike in the 1D Keller-Segel model. Zbl 1133.35058
Kang, K.; Kolokolnikov, T.; Ward, M. J.
2007
Asymptotics beyond all orders for a low Reynolds number flow. Zbl 0880.76022
Keller, Joseph B.; Ward, Michael J.
1996
The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029
Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip
2002
An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion. Zbl 1439.92024
Gou, J.; Ward, M. J.
2016
Hotspot formation and dynamics for a continuum model of urban crime. Zbl 1408.91169
Tse, W. H.; Ward, M. J.
2016
Asymptotics of some nonlinear eigenvalue problems modelling a MEMS capacitor. II: Multiple solutions and singular asymptotics. Zbl 1220.35108
Lindsay, A. E.; Ward, M. J.
2011
Asymptotic analysis of first passage time problems inspired by ecology. Zbl 1319.35275
Kurella, Venu; Tzou, Justin; Coombs, Daniel; Ward, Michael
2015
Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. Zbl 1145.35388
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2006
An asymptotic analysis of localized solutions for some reaction-diffusion model in multidimensional domains. Zbl 0932.35059
Ward, Michael J.
1996
An explicitly solvable nonlocal eigenvalue problem and the stability of a spike for a sub-diffusive reaction-diffusion system. Zbl 1275.35020
Nec, Y.; Ward, M. J.
2013
A hybrid asymptotic-numerical method for low Reynolds number flows past a cylindrical body. Zbl 0854.76028
Kropinski, M. C. A.; Ward, Michael J.; Keller, Joseph B.
1995
Asymptotic methods for reaction-diffusion systems: past and present. Zbl 1334.92004
Ward, Michael J.
2006
Oscillatory dynamics for a coupled membrane-bulk diffusion model with Fitzhugh-Nagumo membrane kinetics. Zbl 1347.35032
Gou, J.; Ward, M. J.
2016
Synchronized oscillatory dynamics for a 1-D model of membrane kinetics coupled by linear bulk diffusion. Zbl 1331.35038
Gou, J.; Li, Y. X.; Nagata, W.; Ward, M. J.
2015
The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. Zbl 1125.35048
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. Zbl 1434.35019
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J.
2017
Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems. Zbl 1338.35246
Moyles, I.; Tse, W. H.; Ward, M. J.
2016
Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems. Zbl 1393.35106
Ward, M. J.
2018
Numerical challenges for resolving spike dynamics for two one-dimensional reaction-diffusion systems. Zbl 1141.35389
Sun, Wentao; Tang, Tao; Ward, Michael J.; Wei, Juncheng
2003
Pulse-splitting for some reaction-diffusion systems in one-space dimension. Zbl 1145.35401
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Metastable internal layer dynamics for the viscous Cahn-Hilliard equation. Zbl 0859.35008
Reyna, Luis G.; Ward, Michael J.
1995
The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities. Zbl 1392.35039
Tzou, J. C.; Ward, M. J.
2018
The stability of localized spikes for the 1-D Brusselator reaction-diffusion model. Zbl 1295.35038
Tzou, J. C.; Nec, Y.; Ward, M. J.
2013
Conditional mean first passage times to small traps in a 3-D domain with a sticky boundary: applications to T cell searching behavior in lymph nodes. Zbl 1339.92009
Delgado, M. I.; Ward, M. J.; Coombs, D.
2015
Asymptotic analysis of localized solutions to some linear and nonlinear biharmonic eigenvalue problems. Zbl 1219.35043
Kropinski, M. C.; Lindsay, A. E.; Ward, M. J.
2011
Metastable patterns, layer collapses, and coarsening for a one- dimensional Ginzburg-Landau equation. Zbl 0794.35119
Ward, Michael J.
1994
A theory of synchrony by coupling through a diffusive chemical signal. Zbl 1376.92020
Gou, Jia; Chiang, Wei-Yin; Lai, Pik-Yin; Ward, Michael J.; Li, Yue-Xian
2017
Asymptotic methods for metal oxide semiconductor field effect transistor modeling. Zbl 0707.35130
Ward, M. J.; Odeh, F. M.; Cohen, D. S.
1990
Multiple steady-state solutions in a multijunction semiconductor device. Zbl 0739.34028
Ward, M. J.; Reyna, L. G.; Odeh, F. M.
1991
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. Zbl 1105.35132
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2006
Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion. Zbl 1252.35033
Nec, Yana; Ward, Michael J.
2012
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Zbl 1063.35084
Kolokolnikov, Theodore; Ward, Michael J.
2004
Internal layers, small eigenvalues, and the sensitivity of metastable motion. Zbl 0818.35008
Ward, Michael J.; Reyna, Luis G.
1995
Dynamic metastability and singular perturbations. Zbl 0910.35011
Ward, Michael J.
1998
An asymptotic study of oxygen transport from multiple capillaries to skeletal muscle tissue. Zbl 0990.92009
Titcombe, Michèle S.; Ward, Michael J.
2000
Spot dynamics in a reaction-diffusion model of plant root hair initiation. Zbl 1383.92048
Avitabile, Daniele; Breña-Medina, Victor F.; Ward, Michael J.
2018
Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in $$\mathbb R^2$$. Zbl 1334.35347
Iron, David; Rumsey, John; Ward, Michael J.; Wei, Juncheng
2014
Self-replication of mesa patterns in reaction-diffusion systems. Zbl 1136.35002
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007
Mathematical modeling of plant root hair initiation: dynamics of localized patches. Zbl 1302.35030
Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J.
2014
The dynamics of drops and attached interfaces for the constrained Allen-Cahn equation. Zbl 0988.76095
Stafford, D.; Ward, M. J.; Wetton, B.
2001
Metastable dynamics and exponential asymptotics in multi-dimensional domains. Zbl 1007.35002
Ward, Michael J.
2001
The stability and dynamics of hot-spot solutions to two one-dimensional microwave heating models. Zbl 1050.35008
Iron, David; Ward, Michael J.
2004
Reaction rate of small diffusing molecules on a cylindrical membrane. Zbl 1206.82150
Straube, Ronny; Ward, Michael J.; Falcke, Martin
2007
The stability and slow dynamics of two-spike patterns for a class of reaction-diffusion system. Zbl 1283.35113
Nec, Y.; Ward, M. J.
2013
Nonlinear eigenvalue problems under strong localized perturbations with applications to chemical reactors. Zbl 0728.65087
Ward, Michael J.; Keller, Joseph B.
1991
An asymptotic analysis of intracellular signaling gradients arising from multiple small compartments. Zbl 1182.92025
Straube, Ronny; Ward, Michael J.
2009
Nonlinear dynamics of a periodically driven Duffing resonator coupled to a van der Pol oscillator. Zbl 1250.34032
Wei, X.; Randrianandrasana, M. F.; Ward, M.; Lowe, D.
2011
Similarity: Generalizations, applications and open problems. Zbl 1188.00015
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.
2010
Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field. Zbl 1446.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2020
Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. Zbl 1434.35017
Moyles, Iain R.; Ward, Michael J.
2017
The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. Zbl 1419.35107
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng
2019
On the asymptotic and numerical analyses of exponentially ill-conditioned singularly perturbed boundary value problems. Zbl 0824.65070
Lee, June-Yub; Ward, Michael J.
1995
Spike pinning for the Gierer-Meinhardt model. Zbl 0979.35142
Iron, David; Ward, Michael J.
2001
A practical method for finite element ring rolling simulation using the ALE flow formulation. Zbl 1125.74383
Davey, K.; Ward, M. J.
2002
The analysis of a two-phase zone with condensation in a porous medium. Zbl 1113.76458
Bridge, L.; Bradean, R.; Ward, M. J.; Wetton, B. R.
2003
Transition to blow-up in a reaction-diffusion model with localized spike solutions. Zbl 1387.35338
Rottschäfer, V.; Tzou, J. C.; Ward, M. J.
2017
Singular perturbations and a free boundary problem in the modeling of field-effect transitors. Zbl 0753.35112
Ward, Michael J.
1992
The onset of thermal runaway in partially insulated or cooled reactors. Zbl 0796.35060
Ward, Michael J.; Van de Velde, Eric F.
1992
Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. Zbl 1428.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2019
Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. Zbl 1146.92005
Bressloff, Paul C.; Earnshaw, Berton A.; Ward, Michael J.
2008
Role of gas- and condensed-phase kinetics in burning rate control of energetic solids. Zbl 0948.74005
Ward, M. J.; Son, S. F.; Brewster, M. Q.
1998
A hybrid method for low Reynolds number flow past an asymmetric cylindrical body. Zbl 1136.76345
Titcombe, Michèle S.; Ward, Michael J.; Kropinski, Mary Catherine
2000
Delayed reaction kinetics and the stability of spikes in the Gierer-Meinhardt model. Zbl 1368.35021
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng
2017
A hybrid asymptotic-numerical method for calculating drag coefficients in 2-D low Reynolds number flows. Zbl 1365.76273
Hormozi, Sarah; Ward, Michael J.
2017
Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. Zbl 1391.35225
Tzou, J. C.; Ward, M. J.; Wei, J. C.
2018
Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field. Zbl 1446.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2020
Stable asymmetric spike equilibria for the Gierer-Meinhardt model with a precursor field. Zbl 1460.35014
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2020
The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. Zbl 1419.35107
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng
2019
Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. Zbl 1428.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2019
Refined stability thresholds for localized spot patterns for the Brusselator model in $$\mathbb{R}^2$$. Zbl 1427.35107
Chang, Y.; Tzou, J. C.; Ward, M. J.; Wei, J. C.
2019
Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems. Zbl 1393.35106
Ward, M. J.
2018
The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities. Zbl 1392.35039
Tzou, J. C.; Ward, M. J.
2018
Spot dynamics in a reaction-diffusion model of plant root hair initiation. Zbl 1383.92048
Avitabile, Daniele; Breña-Medina, Victor F.; Ward, Michael J.
2018
Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. Zbl 1391.35225
Tzou, J. C.; Ward, M. J.; Wei, J. C.
2018
Stabilizing a homoclinic stripe. Zbl 1425.35100
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng
2018
Asynchronous instabilities of crime hotspots for a 1-D reaction-diffusion model of urban crime with focused police patrol. Zbl 1397.35138
Tse, Wang Hung; Ward, Michael J.
2018
First passage statistics for the capture of a Brownian particle by a structured spherical target with multiple surface traps. Zbl 1372.35021
Lindsay, Alan E.; Bernoff, Andrew J.; Ward, Michael J.
2017
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. Zbl 1434.35019
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J.
2017
A theory of synchrony by coupling through a diffusive chemical signal. Zbl 1376.92020
Gou, Jia; Chiang, Wei-Yin; Lai, Pik-Yin; Ward, Michael J.; Li, Yue-Xian
2017
Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. Zbl 1434.35017
Moyles, Iain R.; Ward, Michael J.
2017
Transition to blow-up in a reaction-diffusion model with localized spike solutions. Zbl 1387.35338
Rottschäfer, V.; Tzou, J. C.; Ward, M. J.
2017
Delayed reaction kinetics and the stability of spikes in the Gierer-Meinhardt model. Zbl 1368.35021
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng
2017
A hybrid asymptotic-numerical method for calculating drag coefficients in 2-D low Reynolds number flows. Zbl 1365.76273
Hormozi, Sarah; Ward, Michael J.
2017
Application of quasi-steady-state methods to nonlinear models of intracellular transport by molecular motors. Zbl 1372.92035
Zmurchok, Cole; Small, Tim; Ward, Michael J.; Edelstein-Keshet, Leah
2017
The dynamics of localized spot patterns for reaction-diffusion systems on the sphere. Zbl 1338.35248
Trinh, Philippe H.; Ward, Michael J.
2016
An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion. Zbl 1439.92024
Gou, J.; Ward, M. J.
2016
Hotspot formation and dynamics for a continuum model of urban crime. Zbl 1408.91169
Tse, W. H.; Ward, M. J.
2016
Oscillatory dynamics for a coupled membrane-bulk diffusion model with Fitzhugh-Nagumo membrane kinetics. Zbl 1347.35032
Gou, J.; Ward, M. J.
2016
Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems. Zbl 1338.35246
Moyles, I.; Tse, W. H.; Ward, M. J.
2016
Localized spot patterns on the sphere for reaction-diffusion systems: theory and open problems. Zbl 1357.35189
Jamieson-Lane, Alastair; Trinh, Philippe H.; Ward, Michael J.
2016
Mathematical modelling of crime and security: special issue of EJAM. Zbl 1384.00059
Bertozzi, Andrea L.; Johnson, Shane D.; Ward, Michael J.
2016
Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. Zbl 1364.35151
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T.
2015
Asymptotic analysis of first passage time problems inspired by ecology. Zbl 1319.35275
Kurella, Venu; Tzou, Justin; Coombs, Daniel; Ward, Michael
2015
Synchronized oscillatory dynamics for a 1-D model of membrane kinetics coupled by linear bulk diffusion. Zbl 1331.35038
Gou, J.; Li, Y. X.; Nagata, W.; Ward, M. J.
2015
Conditional mean first passage times to small traps in a 3-D domain with a sticky boundary: applications to T cell searching behavior in lymph nodes. Zbl 1339.92009
Delgado, M. I.; Ward, M. J.; Coombs, D.
2015
The transition to a point constraint in a mixed biharmonic eigenvalue problem. Zbl 1319.35120
Lindsay, A. E.; Ward, M. J.; Kolokolnikov, T.
2015
On accurately estimating stability thresholds for periodic spot patterns of reaction-diffusion systems in $$\mathbb{R}^2$$. Zbl 1382.35134
Iron, D.; Rumsey, J.; Ward, M. J.; Wei, J.
2015
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
The stability of localized spot patterns for the Brusselator on the sphere. Zbl 1302.35033
Rozada, Ignacio; Ruuth, Steven J.; Ward, M. J.
2014
Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in $$\mathbb R^2$$. Zbl 1334.35347
Iron, David; Rumsey, John; Ward, Michael J.; Wei, Juncheng
2014
Mathematical modeling of plant root hair initiation: dynamics of localized patches. Zbl 1302.35030
Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J.
2014
An explicitly solvable nonlocal eigenvalue problem and the stability of a spike for a sub-diffusive reaction-diffusion system. Zbl 1275.35020
Nec, Y.; Ward, M. J.
2013
The stability of localized spikes for the 1-D Brusselator reaction-diffusion model. Zbl 1295.35038
Tzou, J. C.; Nec, Y.; Ward, M. J.
2013
The stability and slow dynamics of two-spike patterns for a class of reaction-diffusion system. Zbl 1283.35113
Nec, Y.; Ward, M. J.
2013
Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion. Zbl 1252.35033
Nec, Yana; Ward, Michael J.
2012
The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033
Chen, W.; Ward, M. J.
2011
Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps. Zbl 1219.35155
Cheviakov, A. F.; Ward, M. J.
2011
Asymptotics of some nonlinear eigenvalue problems modelling a MEMS capacitor. II: Multiple solutions and singular asymptotics. Zbl 1220.35108
Lindsay, A. E.; Ward, M. J.
2011
Asymptotic analysis of localized solutions to some linear and nonlinear biharmonic eigenvalue problems. Zbl 1219.35043
Kropinski, M. C.; Lindsay, A. E.; Ward, M. J.
2011
Nonlinear dynamics of a periodically driven Duffing resonator coupled to a van der Pol oscillator. Zbl 1250.34032
Wei, X.; Randrianandrasana, M. F.; Ward, M.; Lowe, D.
2011
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
An asymptotic analysis of the mean first passage time for narrow escape problems. II: The sphere. Zbl 1204.35030
Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny
2010
Similarity: Generalizations, applications and open problems. Zbl 1188.00015
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.
2010
Asymptotic methods for PDE problems in fluid mechanics and related systems with strong localized perturbations in two dimensional domains. Zbl 1419.76535
Ward, Michael J.; Kropinski, Mary-Catherine
2010
An asymptotic analysis of the persistence threshold for the diffusive logistic model in spatial environments with localized patches. Zbl 1207.35035
Lindsay, Alan E.; Ward, Michael J.
2010
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
Diffusion on a sphere with localized traps: mean first passage time, eigenvalue asymptotics, and Fekete points. Zbl 1191.35032
Coombs, Daniel; Straube, Ronny; Ward, Michael
2009
Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. Zbl 1197.35021
Chen, Wan; Ward, Michael J.
2009
An asymptotic analysis of intracellular signaling gradients arising from multiple small compartments. Zbl 1182.92025
Straube, Ronny; Ward, Michael J.
2009
Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor: Part I: Fold point asymptotics. Zbl 1173.35625
Lindsay, A. E.; Ward, M. J.
2008
Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. Zbl 1146.92005
Bressloff, Paul C.; Earnshaw, Berton A.; Ward, Michael J.
2008
The stability and dynamics of a spike in the 1D Keller-Segel model. Zbl 1133.35058
Kang, K.; Kolokolnikov, T.; Ward, M. J.
2007
Self-replication of mesa patterns in reaction-diffusion systems. Zbl 1136.35002
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007
Reaction rate of small diffusing molecules on a cylindrical membrane. Zbl 1206.82150
Straube, Ronny; Ward, Michael J.; Falcke, Martin
2007
A two-dimensional metastable flame-front and a degenrate spike-layer problem. Zbl 1140.35336
Cheviakov, Alexei F.; Ward, Michael J.
2007
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. Zbl 1145.35388
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2006
Asymptotic methods for reaction-diffusion systems: past and present. Zbl 1334.92004
Ward, Michael J.
2006
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. Zbl 1105.35132
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2006
Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties. Zbl 1103.35042
Guo, Yujin; Pan, Zhenguo; Ward, M. J.
2005
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404
Sun, Wentao; Ward, Michael J.; Russell, Robert
2005
Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Zbl 1090.35070
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J.
2005
The existence and stability of spike patterns in a chemotaxis model. Zbl 1073.35118
Sleeman, B. D.; Ward, Michael J.; Wei, J. C.
2005
The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. Zbl 1125.35048
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Pulse-splitting for some reaction-diffusion systems in one-space dimension. Zbl 1145.35401
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Zbl 1063.35084
Kolokolnikov, Theodore; Ward, Michael J.
2004
The stability and dynamics of hot-spot solutions to two one-dimensional microwave heating models. Zbl 1050.35008
Iron, David; Ward, Michael J.
2004
Spikes for singularly perturbed reaction-diffusion systems and Carrier’s problem. Zbl 1125.35373
Ward, Michael J.
2004
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Zbl 1030.35011
Ward, M. J.; Wei, J.
2003
Hopf bifurction of spike solutions for the shadow Gierer-Meinhardt model. Zbl 1063.35030
Ward, M. J.; Wei, J.
2003
Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. Zbl 1063.35024
Kolokolnikov, Theodore; Ward, Michael J.
2003
Numerical challenges for resolving spike dynamics for two one-dimensional reaction-diffusion systems. Zbl 1141.35389
Sun, Wentao; Tang, Tao; Ward, Michael J.; Wei, Juncheng
2003
The analysis of a two-phase zone with condensation in a porous medium. Zbl 1113.76458
Bridge, L.; Bradean, R.; Ward, M. J.; Wetton, B. R.
2003
The existence and stability of asymmetric spike patterns for the Schnakenberg model. Zbl 1152.35397
Ward, Michael J.; Wei, Juncheng
2002
The dynamics of multispike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 1019.35016
Iron, David; Ward, Michael J.
2002
Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability. Zbl 1010.35002
Ward, M. J.; Wei, J.
2002
The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029
Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip
2002
A practical method for finite element ring rolling simulation using the ALE flow formulation. Zbl 1125.74383
Davey, K.; Ward, M. J.
2002
Thermal runaway and microwave heating in thin cylindrical domains. Zbl 1002.80010
Ward, Michael J.
2002
The stability of spike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 0983.35020
Iron, David; Ward, Michael J.; Wei, Juncheng
2001
The dynamics of drops and attached interfaces for the constrained Allen-Cahn equation. Zbl 0988.76095
Stafford, D.; Ward, M. J.; Wetton, B.
2001
Metastable dynamics and exponential asymptotics in multi-dimensional domains. Zbl 1007.35002
Ward, Michael J.
2001
Spike pinning for the Gierer-Meinhardt model. Zbl 0979.35142
Iron, David; Ward, Michael J.
2001
A metastable spike solution for a nonlocal reaction-diffusion model. Zbl 0956.35011
Iron, David; Ward, Michael J.
2000
Dynamics and coarsening of interfaces for the viscous Cahn-Hilliard equation in one spatial dimension. Zbl 1136.74366
Sun, Xiaodi; Ward, Michael J.
2000
An asymptotic study of oxygen transport from multiple capillaries to skeletal muscle tissue. Zbl 0990.92009
Titcombe, Michèle S.; Ward, Michael J.
2000
A hybrid method for low Reynolds number flow past an asymmetric cylindrical body. Zbl 1136.76345
Titcombe, Michèle S.; Ward, Michael J.; Kropinski, Mary Catherine
2000
An efficient solution method for finite element ring-rolling simulation. Zbl 0990.74061
Davey, K.; Ward, M. J.
2000
The dynamics of boundary spikes for a nonlocal reaction-diffusion model. Zbl 0971.92002
Iron, D.; Ward, M. J.
2000
Diffusion and bifurcation problems in singularly perturbed domains. Zbl 1107.35369
Ward, Michael J.
2000
A successive preconditioned conjugate gradient method for the minimization of quadratic and nonlinear functions. Zbl 0971.65052
Davey, K.; Ward, M. J.
2000
Metastability for a generalized Burgers equation with applications to propagating flame fronts. Zbl 0919.35122
Sun, X.; Ward, M. J.
1999
Summing logarithmic expansions for elliptic equations in multiply-connected domains with small holes. Zbl 0981.76072
Titcombe, Michèle S.; Ward, Michael J.
1999
...and 24 more Documents
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Cited by 827 Authors

 69 Ward, Michael J. 56 Wei, Juncheng 27 Kolokolnikov, Theodore 18 Holcman, David 18 Winter, Matthias 16 Doelman, Arjen 14 Lindsay, Alan E. 14 Tzou, Justin C. 12 Iron, David 11 Lanza de Cristoforis, Massimo 11 Lawley, Sean D. 11 Strani, Marta 10 Chen, Xinfu 10 Laurençot, Philippe 10 Walker, Christoph 8 Rademacher, Jens Diederich Michael 8 Schuss, Zeev 8 van Heijster, Peter 8 Wang, Mingxin 7 Bressloff, Paul C. 7 Nec, Yana 7 Zhou, Jun 6 Folino, Raffaele 6 Horikawa, Yo 6 Maini, Philip Kumar 5 Bertozzi, Andrea Louise 5 Escher, Joachim 5 Ishii, Yuta 5 Musolino, Paolo 5 Shi, Junping 5 Xie, Shuangquan 5 Zhang, Yajing 4 Bastiaansen, Robbin 4 Bernoff, Andrew J. 4 Dalla Riva, Matteo 4 Glasner, Karl B. 4 Gomez, Daniel 4 Gou, Jia 4 Grebenkov, Denis S. 4 Guo, Jong-Shenq 4 Guo, Zongming 4 Hao, Jianghao 4 Hou, Xiaojie 4 Kowalczyk, Michał 4 Krause, Andrew L. 4 Lai, Xin 4 Li, Tong 4 Li, You 4 Lienstromberg, Christina 4 Madzvamuse, Anotida 4 Mascia, Corrado 4 Morimoto, Kotaro 4 Moyles, Iain R. 4 Nagata, Wayne 4 Peng, Rui 4 Qin, Cong 4 Reyna, Luis Guillermo M. 4 Rumsey, John R. 4 Sandstede, Björn 4 Tarzia, Domingo Alberto 4 Tse, Wang Hung 4 Wang, Jinliang 4 Wang, Qi 4 Wetton, Brian R. 3 Ammari, Habib M. 3 Ao, Weiwei 3 Avitabile, Daniele 3 Bates, Peter W. 3 Boukrouche, Mahdi 3 Bramburger, Jason J. 3 Breña-Medina, Víctor F. 3 Brubaker, Nicholas D. 3 Cartailler, J. 3 Carter, Paul M. 3 Champneys, Alan R. 3 Chen, Wenyan 3 Chirilus-Bruckner, Martina 3 Choi, Yongho 3 Choo, S. M. 3 Fan, Jishan 3 Fusco, Giorgio 3 Gaffney, Eamonn A. 3 Gai, Chunyi 3 Kaper, Tasso J. 3 Kavallaris, Nikos I. 3 Kim, Junseok 3 Klika, Václav 3 Kühn, Christian 3 Kupka, Ivan A. K. 3 Lacey, Andrew A. 3 Mei, Linfeng 3 Nikolopoulos, Christos V. 3 Nishiura, Yasumasa 3 O’Malley, Robert E. jun. 3 Paquin-Lefebvre, Frédéric 3 Perthame, Benoît 3 Rottschäfer, Vivi 3 Short, Martin B. 3 Tzou, Leo 3 Volpert, Vitaly A. ...and 727 more Authors
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Cited in 157 Serials

 43 Journal of Differential Equations 30 Physica D 28 European Journal of Applied Mathematics 25 SIAM Journal on Applied Dynamical Systems 24 SIAM Journal on Applied Mathematics 21 Journal of Mathematical Analysis and Applications 21 Journal of Mathematical Biology 19 Journal of Nonlinear Science 18 Bulletin of Mathematical Biology 14 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 Studies in Applied Mathematics 14 Discrete and Continuous Dynamical Systems. Series B 12 Nonlinearity 12 Journal of Dynamics and Differential Equations 11 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Journal of Computational Physics 10 Journal of Fluid Mechanics 10 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 9 Journal of Engineering Mathematics 9 Journal of Statistical Physics 9 Discrete and Continuous Dynamical Systems 9 Nonlinear Analysis. Real World Applications 9 Multiscale Modeling & Simulation 8 Applied Mathematics Letters 8 Chaos 7 Computers & Mathematics with Applications 6 Mathematical and Computer Modelling 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Communications in Nonlinear Science and Numerical Simulation 6 Complex Variables and Elliptic Equations 5 Applied Mathematics and Computation 5 Journal of Scientific Computing 5 Communications on Pure and Applied Analysis 5 Mathematical Modelling of Natural Phenomena 5 Discrete and Continuous Dynamical Systems. Series S 4 Applicable Analysis 4 Mathematical Methods in the Applied Sciences 4 SIAM Journal on Mathematical Analysis 4 SIAM Journal on Scientific Computing 3 Archive for Rational Mechanics and Analysis 3 Journal of Mathematical Physics 3 Chaos, Solitons and Fractals 3 Journal of Computational and Applied Mathematics 3 Numerical Functional Analysis and Optimization 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Applied Numerical Mathematics 3 Japan Journal of Industrial and Applied Mathematics 3 Applied Mathematical Modelling 3 Calculus of Variations and Partial Differential Equations 3 NoDEA. Nonlinear Differential Equations and Applications 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Journal of Theoretical Biology 3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Mathematical Biosciences 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Duke Mathematical Journal 2 Mathematics and Computers in Simulation 2 Quarterly of Applied Mathematics 2 Transactions of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Complexity 2 Neural Networks 2 Physics of Fluids 2 Journal of Mathematical Chemistry 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Discrete Dynamics in Nature and Society 2 Analysis (München) 2 Combustion Theory and Modelling 2 Communications in Contemporary Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Applied Mathematics and Computing 2 Mathematical Biosciences and Engineering 2 Boundary Value Problems 2 Waves in Random and Complex Media 2 Journal of Physics A: Mathematical and Theoretical 2 Science China. Mathematics 2 The Journal of Mathematical Neuroscience 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Journal of Elliptic and Parabolic Equations 1 Acta Mechanica 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 Physica A 1 Physics Reports 1 Reviews of Modern Physics 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Polonici Mathematici 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Integral Equations and Operator Theory ...and 57 more Serials
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Cited in 35 Fields

 489 Partial differential equations (35-XX) 205 Biology and other natural sciences (92-XX) 72 Numerical analysis (65-XX) 69 Ordinary differential equations (34-XX) 54 Fluid mechanics (76-XX) 48 Dynamical systems and ergodic theory (37-XX) 46 Probability theory and stochastic processes (60-XX) 43 Mechanics of deformable solids (74-XX) 32 Statistical mechanics, structure of matter (82-XX) 24 Optics, electromagnetic theory (78-XX) 22 Operator theory (47-XX) 18 Classical thermodynamics, heat transfer (80-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Integral equations (45-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 10 Potential theory (31-XX) 6 Quantum theory (81-XX) 5 Mechanics of particles and systems (70-XX) 4 Differential geometry (53-XX) 4 Systems theory; control (93-XX) 3 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Geophysics (86-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX)