Differential and Integral Equations

Asymptotic profiles of variational solutions for a FitzHugh-Nagumo-type elliptic system

Hiroshi Matsuzawa

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Abstract

In this paper we consider a semilinear elliptic system of FitzHugh-Nagumo type on a bounded domain with the same diffusion constant $\lambda^{-1}$ under the Dirichlet boundary condition $-\Delta u=\lambda(f(u)-v)$, $-\Delta v=\lambda(\delta u-\gamma v)$ in $\Omega$. In some parameter range on $(\delta, \gamma)$ this system has at least two nontrivial solutions when $\lambda$ is sufficiently large, and these solutions are obtained by variational methods. We study the asymptotic profiles of these solutions for large $\lambda$ in some parameter range on $(\delta, \gamma)$, especially for small $\delta$ and large $\gamma$.

Article information

Source
Differential Integral Equations, Volume 16, Number 8 (2003), 897-926.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060575

Mathematical Reviews number (MathSciNet)
MR1988952

Zentralblatt MATH identifier
1066.35030

Subjects
Primary: 35J55
Secondary: 35B40: Asymptotic behavior of solutions 35J50: Variational methods for elliptic systems 35J60: Nonlinear elliptic equations 35K57: Reaction-diffusion equations

Citation

Matsuzawa, Hiroshi. Asymptotic profiles of variational solutions for a FitzHugh-Nagumo-type elliptic system. Differential Integral Equations 16 (2003), no. 8, 897--926. https://projecteuclid.org/euclid.die/1356060575


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