Decay at infinity for parabolic equations

2005/09/09 by Oliver C. Schnürer, Schnürer, Oliver C., Hartmut Schwetlick +2
Computer Science · Mathematics · #35B40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35B40

paper · pdf · doi:10.48550/arxiv.math/0509212

7 pages

arxiv created 2005/09/09 · openalex publication_date 2005/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider solutions to linear parabolic equations with initial data decaying at spatial infinity. For a class of advection-diffusion equations with a spatially dependent velocity field, we study the behavior of solutions as time tends to infinity. We characterize velocity fields, so that positive solutions decay or lift-off at spatial infinity as time tends to infinity. This addresses the question of stability of the zero solution for decaying perturbations.

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