Journal title
Applicable Analysis and Discrete Mathematics
Issue
3
Volume
13
Last updated
2024-04-10T07:44:16.25+01:00
Abstract
This paper is concerned with the proof of existence and numerical approximation of large-data global-in-time Young measure solutions to initial-boundaryvalue problems for multidimensional nonlinear parabolic systems of forwardbackward type of the form Btu ´ divpapDuqq ` Bu “ F, where B P R mˆm, Bv ¨ v ě 0 for all v P R m, F is an m-component vector-function defined on a bounded open Lipschitz domain Ω Ă R n , and a is a locally Lipschitz mapping of the form apAq “ KpAqA, where K : R mˆn Ñ R. The function a may have unequal lower and upper growth rates; it is not assumed to be monotone, nor is it assumed to be the gradient of a potential. We construct a numerical method for the approximate solution of problems in this class, and we prove its convergence to a Young measure solution of the system.
Symplectic ID
974176
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Publication type
Journal Article
Publication date
27 Aug 2019