Asymptotic stability of traveling wave solutions for perturbations with algebraic decay

Details Asymptotic stability of traveling wave solutions for perturbations with algebraic decay Asymptotic stability of traveling wave solutions for perturbations with algebraic decay

2001-03-02

arxiv.org/abs/math/0103012v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation of the traveling wave profile decays at an algebraic rate, then the solution is shown to converge to a shifted wave profile at a corresponding temporal algebraic rate, and optimal intermediate results that combine temporal and spatial decay are obtained. The proofs are based on a general interpolation principle which says that algebraic decay results of this form always follow if exponential temporal decay holds for perturbation with exponential spatial decay and the wave profile is stable for general perturbations.

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