Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 71, Number 2 (2019), 243-279.
Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor
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.
Tohoku Math. J. (2), Volume 71, Number 2 (2019), 243-279.
First available in Project Euclid: 21 June 2019
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Li, Ying; Marciniak-Czochra, Anna; Takagi, Izumi; Wu, Boying. Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor. Tohoku Math. J. (2) 71 (2019), no. 2, 243--279. doi:10.2748/tmj/1561082598. https://projecteuclid.org/euclid.tmj/1561082598