Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems

DOI10.3934/dcdsb.2014.19.697zbMath1292.35022OpenAlexW2327235471MaRDI QIDQ2438872

Hirokazu Ninomiya, Yoshihito Kohsaka, Yan-Yu Chen

Publication date: 7 March 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.697

zbMATH Keywords

interface equationactivator-inhibitor systemFitzHugh-Nagumo system

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Free boundary problems for PDEs (35R35) Initial value problems for second-order parabolic systems (35K45) Traveling wave solutions (35C07) Semilinear parabolic equations (35K58)

Related Items (7)

Global existence and uniqueness of solutions for one-dimensional reaction-interface systems ⋮ Existence of rotating spots with spatially dependent feedback in the plane in a wave front interaction model ⋮ Traveling spots on multi-dimensional excitable media ⋮ Weak entire solutions of reaction-interface systems ⋮ Traveling Curved Waves in Two-Dimensional Excitable Media ⋮ Compact traveling waves for anisotropic curvature flows with driving force ⋮ Global Dynamics on One-Dimensional Excitable Media

Cites Work

• Motion of level sets by mean curvature. I
• Higher-dimensional localized patterns in excitable media
• Existence and uniqueness of rigidly rotating spiral waves by a wave front interaction model
• Existence of a rotating wave pattern in a disk for a wave front interaction model
• Existence and uniqueness of stabilized propagating wave segments in wave front interaction model
• Pattern formation in non-gradient reaction-diffusion systems: the effects of front bifurcations
• Ordinary Differential Equations

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