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Allen-Cahn equation with strong irreversibility.

Euro. J. of Applied Mathematics 30, 707-755 (2018)
Publ. Version/Full Text Postprint DOI
Open Access Green
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 -> +infinity.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Strongly Irreversible Evolution Equation ; Allen-cahn Equation ; Obstacle Parabolic Problem ; Global Attractor ; Omega-limit Set ; Partial Energy-dissipation; Quasi-static Evolution; Damage; Approximation; Existence; Model; Boundary; Systems; Growth
ISSN (print) / ISBN 0956-7925
e-ISSN 0956-7925
Quellenangaben Volume: 30, Issue: 4, Pages: 707-755 Article Number: , Supplement: ,
Publisher Cambridge Univ. Press
Publishing Place New York, NY
Reviewing status