Numerical approximation of young-measure solutions to parabolic systems of forward-backward type

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 ¨...

Ful tanımlama

Detaylı Bibliyografya
Asıl Yazarlar: Caddick, M, Suli, E
Materyal Türü: Journal article
Baskı/Yayın Bilgisi: University of Belgrade - School of Electrical Engineering 2019
_version_ 1826269922989178880
author Caddick, M
Suli, E
author_facet Caddick, M
Suli, E
author_sort Caddick, M
collection OXFORD
description 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.
first_indexed 2024-03-06T21:32:47Z
format Journal article
id oxford-uuid:453bbc44-db6f-44bd-b869-0719bf472fb2
institution University of Oxford
last_indexed 2024-03-06T21:32:47Z
publishDate 2019
publisher University of Belgrade - School of Electrical Engineering
record_format dspace
spelling oxford-uuid:453bbc44-db6f-44bd-b869-0719bf472fb22022-03-26T15:06:37ZNumerical approximation of young-measure solutions to parabolic systems of forward-backward typeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:453bbc44-db6f-44bd-b869-0719bf472fb2Symplectic Elements at OxfordUniversity of Belgrade - School of Electrical Engineering2019Caddick, MSuli, EThis 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.
spellingShingle Caddick, M
Suli, E
Numerical approximation of young-measure solutions to parabolic systems of forward-backward type
title Numerical approximation of young-measure solutions to parabolic systems of forward-backward type
title_full Numerical approximation of young-measure solutions to parabolic systems of forward-backward type
title_fullStr Numerical approximation of young-measure solutions to parabolic systems of forward-backward type
title_full_unstemmed Numerical approximation of young-measure solutions to parabolic systems of forward-backward type
title_short Numerical approximation of young-measure solutions to parabolic systems of forward-backward type
title_sort numerical approximation of young measure solutions to parabolic systems of forward backward type
work_keys_str_mv AT caddickm numericalapproximationofyoungmeasuresolutionstoparabolicsystemsofforwardbackwardtype
AT sulie numericalapproximationofyoungmeasuresolutionstoparabolicsystemsofforwardbackwardtype