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Volume 32, Issue 1
Evans Functions and Instability of a Standing Pulse Solution of a Nonlinear System of Reaction Diffusion Equations

Linghai Zhang

Ann. Appl. Math., 32 (2016), pp. 79-101.

Published online: 2022-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35Q20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-32-79, author = {Zhang , Linghai}, title = {Evans Functions and Instability of a Standing Pulse Solution of a Nonlinear System of Reaction Diffusion Equations}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {32}, number = {1}, pages = {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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20630.html} }
TY - JOUR T1 - Evans Functions and Instability of a Standing Pulse Solution of a Nonlinear System of Reaction Diffusion Equations AU - Zhang , Linghai JO - Annals of Applied Mathematics VL - 1 SP - 79 EP - 101 PY - 2022 DA - 2022/06 SN - 32 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20630.html KW - nonlinear system of reaction diffusion equations, standing pulse solutions, existence, instability, linearized stability criterion, Evans functions. AB -

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.

Linghai Zhang. (2022). Evans Functions and Instability of a Standing Pulse Solution of a Nonlinear System of Reaction Diffusion Equations. Annals of Applied Mathematics. 32 (1). 79-101. doi:
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