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 - <p style="text-align: justify; margin-bottom: 5px;">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.<br/>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.</p>