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

Abstract : In this paper, we observe how the heat equation in a noncylindrical 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 [Alvarez-Caudevilla and Lemenant, Adv. Differ. Equ. 15 (2010) 649-688]. We provide a strong convergence result for the solution by use of energetic methods and Γ-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.
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Submitted on : Thursday, September 3, 2020 - 10:06:15 PM
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Pablo Àlvarez-Caudevilla, Matthieu Bonnivard, Antoine Lemenant. Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26, pp.50. ⟨10.1051/cocv/2019023⟩. ⟨hal-02929871⟩

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