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2019 Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor
Ying Li, Anna Marciniak-Czochra, Izumi Takagi, Boying Wu
Tohoku Math. J. (2) 71(2): 243-279 (2019). DOI: 10.2748/tmj/1561082598

Abstract

In this paper, we consider a diffusion equation coupled to an ordinary differential equation with FitzHugh-Nagumo type nonlinearity. We construct continuous spatially heterogeneous steady states near, as well as far from, constant steady states and show that they are all unstable. In addition, we construct various types of steady states with jump discontinuities and prove that they are stable in a weak sense defined by Weinberger.The results are quite different from those for classical reaction-diffusion systems where all species diffuse.

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Ying Li. Anna Marciniak-Czochra. Izumi Takagi. Boying Wu. "Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor." Tohoku Math. J. (2) 71 (2) 243 - 279, 2019. https://doi.org/10.2748/tmj/1561082598

Information

Published: 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07108039
MathSciNet: MR3973251
Digital Object Identifier: 10.2748/tmj/1561082598

Subjects:
Primary: 35B36
Secondary: 35B35, 35K57

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 2 • 2019
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