Decay at infinity for parabolic equations

Oliver C. Schnürer; Hartmut R. Schwetlick

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Decay at infinity for parabolic equations

Oliver C. Schnürer·Hartmut R. Schwetlick

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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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Oliver C. Schnürer, Hartmut R. Schwetlick. 2005-09-09. Decay at infinity for parabolic equations. https://arxiv.org/abs/math/0509212

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