Asymptotic stability of traveling wave solutions for perturbations with algebraic decay

[摘要] 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. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-10

[关键词] generalized Burgers equation;generalized Korteweg-de Vries-Burgers equation;traveling wave;stability;weighted norm