Dr Matthias Winter

Senior Lecturer

Publications

Journals

(2009) Wei, J. and Winter, M., Strongly Interacting Bumps for the Schrödinger-Newton Equations, Journal of Mathematical Physics 50 (1) : 012905 BURA

(2008) Wei, J. and Winter, M., Stationary Multiple Spots for Reaction-Diffusion Systems, Journal of Mathematical Biology 1 : 53-89 BURA

(2008) Wei, J. and Winter, M., Mutually Exclusive Spiky Pattern and Segmentation Modeled by the Five-Component Meinhardt-Gierer System, SIAM J. Appl. Math. 69 (2) : 419-452 BURA

(2008) Winter, M., Wei, J. and Tse, W., Spikes for the Gierer-Meinhardt System with Many Segments of Different Diffusivities, Bulletin of the Institute of Mathematics Academia Sinica New Series 4 (1) : 567-584 BURA

(2007) Maini, P.K., Wei, J. and Winter, M., Stability of Spikes in the Shadow Gierer-Meinhardt System with Robin Boundary Conditions, Chaos: An Interdisciplinary Journal of Nonlinear Science 17 (037106) BURA

(2007) Norbury, J., Wei, J. and Winter, M., Stability of Patterns with Arbitrary Period for a Ginzburg-Landau Equation with a Mean Field, European Journal of Applied Mathematics 18 (2) : 129-151 BURA

(2007) Wei, J. and Winter, M., Symmetric and Asymetric Multiple Clusters in a Reaction-Diffusion System, NoDEA. Nonlinear Differential Equations and Applications 14 (5-6) : 787-823 BURA

(2007) Wei, J. and Winter, M., Existence, Classification and Stability Analysis of Multiple-peaked Solutions for the Gierer-Meinhardt System in R1, Methods and Applications of Analysis 14 (2) : 119-163 BURA

(2006) Wei, J. and Winter, M., Standing Waves in the FitzHugh-Nagumo System and a Problem in Combinatorial Geometry, Mathematische Zeitschrift 254 (2) : 359-383 BURA

(2005) Wei, J. and Winter, M., On A Cubic-Quintic Ginzburg-Landau Equation With Global Coupling, Proceedings of the American Mathematical Society 133 : 1787-1796 BURA

(2005) Wei, J. and Winter, M., Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball, Indiana University Mathematics Journal 54 (3) : 707-742 BURA

(2005) Wei, J. and Winter, M., Clustered Spots in the FitzHugh-Nagumo System, Journal of Differential Equations 213 (1) : 121-145 BURA

(2005) Wei, J., Winter, M. and Yeung, W.K., A Higher-Order Energy Expansion to Two-Dimensional Singularity Perturbed Neumann Problems, Asymptotic Analysis 43 (1-2) : 75-110 BURA

(2004) Iron, D., Wei, J. and Winter, M., Stability Analysis of Turing Patterns Generated by the Schnakenberg Model, Journal of Mathematical Biology 49 (4) : 358-390 BURA

(2004) Wei, J. and Winter, M., On the Gierer-Meinhardt System with Saturation, Communications in Contemporary Mathematics 6 (2) : 259-277 BURA

(2004) Wei, J. and Winter, M., Higher-Order Energy Expansions and Spike Locations, Calculus of Variations and Partial Differential Equations 20 (4) : 403-430 BURA

(2004) Wei, J. and Winter, M., Existence and Stability Analysis of Asymmetric Patterns for the Gierer-Meinhardt System, Journal de Mathematiques Pures et Appliquees 83 (4) : 433-476 BURA

(2003) Wei, J. and Winter, M., Asymmetric Spotty Patterns for the Gray-Scott Model in R2, Studies in Applied Mathematics 110 (1) : 63-102 BURA

(2003) Wei, J. and Winter, M., Existence and Stability of Multiple-Spot Solutions for the Gray-Scott Model in R2, Physica D 176 (3-4) : 147-180 BURA

(2003) Wei, J. and Winter, M., A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction-Diffusion Systems with Fractional Reaction Rates, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 13 (6) : 1529-1543 BURA

(2003) Wei, J. and Winter, M., Higher-Order Energy Expansions for Some Singularly Perturbed Neumann Problems, Comptes Rendus de l'Académie des Sciences. Série I. Mathématique 337 : 37-42 BURA

(2003) Wei, J. and Winter, M., Stability of Monotone Solutions for the Shadow Gierer-Meinhardt System with Finite Diffusivity, Differential Integral Equations 16 (10) : 1153-1180 BURA

(2002) Ball, J.M., Taheri, A. and Winter, M., Local Minimizers in Micromagnetics and Related Problems, Calculus of Variations and Partial Differential Equations 14 (1) : 1-27 BURA

(2002) Norbury, J., Wei, J. and Winter, M., Existence and Stability of Singular Patterns in a Ginzburg-Landau Equation Coupled with a Mean Field, Nonlinearity 15 (6) : 2077-2096 BURA

(2002) Wei, J. and Winter, M., Spikes for the Gierer-Meinhardt System in Two Dimensions: The Strong Coupling Case, Journal of Differential Equations 178 (2) : 478-518 BURA

(2002) Wei, J. and Winter, M., Critical Threshold and Stability of Cluster Solutions for Large Reaction-Diffusion Systems in R, SIAM Journal on Mathematical Analysis 33 (5) : 1058-1089 BURA

(2001) Wei, J. and Winter, M., Spikes for the Two-Dimensional Gierer-Meinhardt System: The Weak Coupling Case, Journal of Nonlinear Science 11 (6) : 415-458 BURA

(2001) Wei, J. and Winter, M., On a Hypercycle System with Nonlinear Rate, Methods and Applications of Analysis 8 (2) : 257-278 BURA

(2001) Wei, J. and Winter, M., Solutions for the Cahn-Hilliard Equation with Many Boundary Spike Layers, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 131 : 185-204 BURA

Chapter in a Book

(2005) Wei, J. and Winter, M., Existence and Stability of Mutiple Spot Solutions for the Gray-Scott Model in R2, EQUADIFF 2003

Others

(2007) Winter, M. and Wei, J., The Role of Boundary Conditions for the Existence and Stability of Spikes for the Gierer-Meinhardt System, IMS Workshop on PDEs

(2007) Winter, M. and Wei, J., Spikes for Biological Systems: The Role of Boundary Conditions, CMS-MITACS Joint Conference

(2006) Winter, M. and Wei, J., Mutually Exclusive Spikes for a Five-Component System of Meinhardt and Gierer, MAFELAP Conference

(2006) Winter, M. and Wei, J., Mutually Exclusive Spikes for a Five-Component System of Meinhardt and Gierer, 6th International AIMS Conference on Dynamical Systems, Differential Equations and Applications

(2005) Winter, M. and Wei, J., Spikes for the Gierer-Meinhardt System - Analysis and Numerical Simulation, Joint DMV-AMS-OMG Conference

(2005) Winter, M. and Wei, J., Spikes for the Gierer-Meinhardt System - Analysis and Numerical Simulation, Oberwolfach Workshop on Topological and Variational Methods for Differential Equations

(2005) Winter, M. and Wei, J., Standing Waves in the FitzHugh-Nagumo System and a Problem in Combinatorial Geometry, Topological and Variational Methods in PDE, CIMAT

(2003) Wei, J. and Winter, M., Existence and Stability of Multiple Spot Solutions for the Gray-Scott Model in R2, EquaDiff

(2003) Winter, M. and Wei, J., Multiple Spikes in Biological Systems, Multiscale Systems and Applications Workshop

(2003) Winter, M. and Wei, J., Higher-Order Energy Expansions for Some Singulary Perturbed Neumann Problem, International Congress on Industrial and Applied Mathematics (ICIAM)

(2003) Winter, M. and Wei, J., Concentrated Solutions for the One- and Two-Dimensional Gierer-Meinhardt System, International Congress on Industrial and Applied Mathematics (ICIAM)

(2003) Winter, M. and Wei, J., Existence and Stability of Multiple Spotty Patterns for the Gray-Scott System in a Two-Dimensional Domain, International Congress on Industrial and Applied Mathematics (ICIAM)

(2003) Winter, M. and Wei, J., On the Shadow Gierer-Meinhardt System with Finite Epsilon, International Congress on Industrial and Applied Mathematics (ICIAM)

(2001) Winter, M. and Wei, J., Concentrated Solutions for the Two-Dimensional Gierer-Meinhardt Systems, Nonlinear Partial Differential Equations Program, PIMS