Higher-dimensional stationary solutions of a FitzHugh-Nagumo system for pattern formation in a spatially heterogeneous medium

Conghui Zhang, Hanzhi Zhang, Shanbing Li*, Gaihui Guo

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

摘要

The aim of this paper is to study pattern formation of a reaction-diffusion-ODE system with FitzHugh-Nagumo type nonlinearity in higher-dimensional domains. We construct continuous steady states, which are close to the equilibria of the kinetic system (i.e., without diffusion) by applying the sub- and super-solution method. In addition, we construct steady states with jump discontinuity via the generalized mountain pass lemma and show that they are asymptotically stable. Moreover, the existence of single transition layer solutions is proved by using the approaches of the singular perturbation method and the generalized implicit function theorems. Finally, we present some numerical simulations to illustrate the theoretical results.

源语言英语
页(从-至)411-446
页数36
期刊Journal of Differential Equations
421
DOI
出版状态已出版 - 15 3月 2025

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引用此

Zhang, C., Zhang, H., Li, S., & Guo, G. (2025). Higher-dimensional stationary solutions of a FitzHugh-Nagumo system for pattern formation in a spatially heterogeneous medium. Journal of Differential Equations, 421, 411-446. https://doi.org/10.1016/j.jde.2024.12.024