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2003 Asymptotic profiles of variational solutions for a FitzHugh-Nagumo-type elliptic system
Hiroshi Matsuzawa
Differential Integral Equations 16(8): 897-926 (2003).

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 $\gamma$.

Citation

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Hiroshi Matsuzawa. "Asymptotic profiles of variational solutions for a FitzHugh-Nagumo-type elliptic system." Differential Integral Equations 16 (8) 897 - 926, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1066.35030
MathSciNet: MR1988952

Subjects:
Primary: 35J55
Secondary: 35B40 , 35J50 , 35J60 , 35K57

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 8 • 2003
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