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• W4387094088 abstract "In this paper, we consider a reaction-diffusion system with mechanical deformation of medium. This system consists of an excitable system bidirectionally coupled with an elasticity equation. The main content consists of two parts. First, for γ>0 sufficiently small, simple pulse of homoclinic type exists. We prove that the traveling pulse is linearly stable. Specifically, there is at most one nontrivial eigenvalue near the origin and it is negative. Second, for γ>0 large, we show existence of double twisted front-back wave loop, indicating bifurcations of various complicated traveling waves, including N-front, N-back and wave train. Then we prove that N-fronts are linearly stable. Our arguments are mainly based on geometric singular perturbation theory, exponential dichotomy, heteroclinic bifurcation and the Melnikov method." @default.
• W4387094088 created "2023-09-28" @default.
• W4387094088 creator A5027834024 @default.
• W4387094088 creator A5063398387 @default.
• W4387094088 date "2023-12-01" @default.
• W4387094088 modified "2023-10-12" @default.
• W4387094088 title "Simple and multiple traveling waves in a reaction-diffusion-mechanics model" @default.
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• W4387094088 doi "https://doi.org/10.1016/j.jde.2023.09.022" @default.
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