Calculus of Variations and Geometric Measure Theory
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P. Álvarez-Caudevilla - M. Bonnivard - A. Lemenant

Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials

created by lemenant on 10 Apr 2018

[BibTeX]

preprint

Inserted: 10 apr 2018
Last Updated: 10 apr 2018

Year: 2018

Abstract:

In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a parabolic version of a previous work by the first and last authors, concerning the stationary case~\cite{PaAn}. We provide a strong convergence result for the solution by use of energetic methods and $\Gamma$-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument by B. Simon.


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