Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system

Details Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system

1994-03-18

arxiv.org/abs/patt-sol/9403002v1

Nonlinear Sciences

Chaotic Dynamics

50 pages in AMSLatex

Scientific paper

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order in $\epsilon$. The formal solution shows that there is an invariant manifold of wave-front-like solutions that attracts other nearby solutions. With an additional assumption on the sign of the wave speed, the wave-front-like solutions converge slowly to stable stationary solutions on that manifold.

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