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arXiv · 2401.14249

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

Pablo Àlvarez-Caudevilla·Matthieu Bonnivard·Antoine Lemenant
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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. 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 due to B. Simon.

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Pablo Àlvarez-Caudevilla, Matthieu Bonnivard, Antoine Lemenant. 2024-01-25. Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials. https://doi.org/10.1051/cocv%2F2019023

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