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

Pablò Alvarez-Caudevilla (1) , Matthieu Bonnivard (2) , Antoine Lemenant (2)

1 Université Carlos III de Madrid
2 LJLL - Laboratoire Jacques-Louis Lions

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 [3]. 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 by B. Simon.

Domaines: Mathématiques générales [math.GM]

Pablò Alvarez-Caudevilla, Matthieu Bonnivard, Antoine Lemenant. Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials. 2018. ⟨hal-01762688⟩