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 ¨...
| Auteurs principaux: | , |
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| Format: | Journal article |
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University of Belgrade - School of Electrical Engineering
2019
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| _version_ | 1826269922989178880 |
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| 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 |