Decay at infinity for parabolic equations

Oliver C. Schnürer; Hartmut R. Schwetlick

Decay at infinity for parabolic equations

偏微分方程分析 2007-05-23 v1

作者: Oliver C. Schnürer , Hartmut R. Schwetlick

摘要

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.

关键词

energy decay for wave equations parabolic partial differential equations nonlinear diffusion equations

引用

@article{arxiv.math/0509212,
  title  = {Decay at infinity for parabolic equations},
  author = {Oliver C. Schnürer and Hartmut R. Schwetlick},
  journal= {arXiv preprint arXiv:math/0509212},
  year   = {2007}
}

备注

7 pages

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