Evans Functions and Instability of a Standing Pulse Solution of a Nonlinear System of Reaction Diffusion Equations

Evans Functions and Instability of a Standing Pulse Solution of a Nonlinear System of Reaction Diffusion Equations

Year:    2016

Author:    Linghai Zhang

Annals of Applied Mathematics, Vol. 32 (2016), Iss. 1 : pp. 79–101

Abstract

In this paper, we consider a nonlinear system of reaction diffusion equations arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients.
The main purpose is to couple together linearized stability criterion (the equivalence of the nonlinear stability, the linear stability and the spectral stability of the standing pulse solutions) and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equations. The Evans functions for the standing pulse solutions are constructed explicitly.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2016-AAM-20630

Annals of Applied Mathematics, Vol. 32 (2016), Iss. 1 : pp. 79–101

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    nonlinear system of reaction diffusion equations standing pulse solutions existence instability linearized stability criterion Evans functions.

Author Details

Linghai Zhang