Allen-Cahn equation with strong irreversibility

Goro Akagi, Messoud Efendiev

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is concerned with a fully non-linear variant of the Allen-Cahn equation with strong irreversibility, where each solution is constrained to be non-decreasing in time. The main purposes of this paper are to prove the well-posedness, smoothing effect and comparison principle, to provide an equivalent reformulation of the equation as a parabolic obstacle problem and to reveal long-time behaviours of solutions. More precisely, by deriving partial energy-dissipation estimates, a global attractor is constructed in a metric setting, and it is also proved that each solution u(x,t) converges to a solution of an elliptic obstacle problem as t → +∞.

Original languageEnglish
Pages (from-to)707-755
Number of pages49
JournalEuropean Journal of Applied Mathematics
Volume30
Issue number4
DOIs
Publication statusPublished - 2019 Aug 1

Keywords

  • Allen-Cahn equation
  • Strongly irreversible evolution equation
  • global attractor
  • obstacle parabolic problem
  • partial energy-dissipation
  • ω-limit set

ASJC Scopus subject areas

  • Applied Mathematics

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