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Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint.
Non. diff. equat. app. 26:10 (2019)
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage Mechanics, is reformulated as a mixed form of two different types of doubly nonlinear evolution equations. Global (in time) solutions to some approximate problems are constructed by performing a time discretization argument and by taking advantage of energy techniques based on specific structures of the equation. Moreover, a variational comparison principle for (possibly non-unique) approximate solutions is established and it also enables us to obtain a local solution as a limit of approximate ones.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Unidirectional Evolution ; Mixed Doubly Nonlinear Equations ; Variational Comparison Principle ; Porous Medium Equation ; Blow-up In Finite Time; Damage Propagation; Well-posedness; Evolution; Model; Existence; System; Behavior
ISSN (print) / ISBN 1021-9722
Quellenangaben Volume: 26, Issue: 2, Article Number: 10
Publishing Place Basel
Institute(s) Institute of Computational Biology (ICB)