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November 2003 Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity
N. N. Nefedov, K. Sakamoto
Hiroshima Math. J. 33(3): 391-432 (November 2003). DOI: 10.32917/hmj/1150997983

Abstract

We deal with reaction-diffusion equations of bistable type in an inhomogeneous medium. When the reaction term is balanced in the sense that a bulk potential energy attains the same global minimum at the two stable equilibria for each spatial point, we derive a free-boundary problem whose solutions determine equilibirum interfaces. We show that a non-degenerate solution of the free-boundary problem gives rise to an equilibrium internal layer solution of the reaction-diffusion equation, and moreover, the stability property of the latter is obtained from a linearization of the free boundary problem.

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N. N. Nefedov. K. Sakamoto. "Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity." Hiroshima Math. J. 33 (3) 391 - 432, November 2003. https://doi.org/10.32917/hmj/1150997983

Information

Published: November 2003
First available in Project Euclid: 22 June 2006

zbMATH: 1065.35039
MathSciNet: MR2040906
Digital Object Identifier: 10.32917/hmj/1150997983

Subjects:
Primary: 35K57
Secondary: 35B25, 35B35

Rights: Copyright © 2003 Hiroshima University, Mathematics Program

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Vol.33 • No. 3 • November 2003
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