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Eigenfunctions of the adjoint operator associatead with a pulse solution of some reaction-diffusion systems
by Shin-Ichiro Ei   Hideo Ikeda   Kota Ikeda   Eiji Yanagida

Vol. 3 No. 4 (2008) P.603~P.666

ABSTRACT

In this paper, we consider the FitzHugh-Nagumo system and obtain by singular perturbation techniques a precise form of the eigenfunction of the adjoint operator associated with the linearization at a traveling pulse solution. We also show that some precise properties of the adjoint eigenfunction are useful to study the behavior of solutions such as interfacial dynamics, the interaction of traveling pulses and so on.

KEYWORDS
Reaction diffusion systems, singular perturbation, stability, traveling wave solution, adjoint system

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 34L99, 35K57, 35B25, 35Q80

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