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

publication date

  • September 2020

start page

  • 1

end page

  • 20

issue

  • 50

volume

  • 26

International Standard Serial Number (ISSN)

  • 1292-8119

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 Gamma-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.

keywords

  • parabolic problems / gamma-convergence / energetic methods / variational methods / partial differential equations