2001/03/02 by Hans Engler, Engler, Hans
Mathematics · Physics and Astronomy · #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35Q53
paper · pdf · doi:10.48550/arxiv.math/0103012
14 pages
arxiv created 2001/03/02 · openalex publication_date 2001/03/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.