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Unidirectional evolution equations of diffusion type.
J. Differ. Equations 266, 1-43 (2019)
This paper is concerned with the uniqueness, existence, partial smoothing effect, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of solutions is proved in an L-2-framework by employing a backward Euler scheme and by introducing a new method of a priori estimates based on a reduction of discretized equations to variational inequalities of obstacle type and by developing a regularity theory for such obstacle problems. The novel discretization argument will be also applied to prove the comparison principle as well as to investigate the long-time behavior of solutions. (C) 2018 Elsevier Inc. All rights reserved.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Unidirectional Diffusion Equation ; Damage Mechanics ; Discretization ; Variational Inequality Of Obstacle Type ; Regularity ; Subdifferential Calculus; Doubly Nonlinear Evolution; Crack-propagation; Well-posedness; Model; Damage; Approximation; Existence; Functionals; Behavior
ISSN (print) / ISBN
0022-0396
e-ISSN
1090-2732
Quellenangaben
Volume: 266,
Issue: 1,
Pages: 1-43
Publisher
Elsevier
Publishing Place
525 B St, Ste 1900, San Diego, Ca 92101-4495 Usa
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)