On Solutions of a Parabolic Equation with Nonstandard Growth Condition
A parabolic equation with nonstandard growth condition is considered. A kind of weak solution and a kind of strong solution are introduced, respectively; the existence of solutions is proved by a parabolically regularized method. The stability of weak solutions is based on a natural partial boundary...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/9397620 |
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| _version_ | 1832566403882811392 |
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| author | Huashui Zhan |
| author_facet | Huashui Zhan |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | A parabolic equation with nonstandard growth condition is considered. A kind of weak solution and a kind of strong solution are introduced, respectively; the existence of solutions is proved by a parabolically regularized method. The stability of weak solutions is based on a natural partial boundary value condition. Two novelty elements of the paper are both the dependence of diffusion coefficient bx,t on the time variable t, and the partial boundary value condition based on a submanifold of ∂Ω×0,T. How to overcome the difficulties arising from the nonstandard growth conditions is another technological novelty of this paper. |
| format | Article |
| id | doaj-art-58e9b585815f4f1ba74aa07fdd740efa |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-58e9b585815f4f1ba74aa07fdd740efa2025-02-03T01:04:08ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/93976209397620On Solutions of a Parabolic Equation with Nonstandard Growth ConditionHuashui Zhan0School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaA parabolic equation with nonstandard growth condition is considered. A kind of weak solution and a kind of strong solution are introduced, respectively; the existence of solutions is proved by a parabolically regularized method. The stability of weak solutions is based on a natural partial boundary value condition. Two novelty elements of the paper are both the dependence of diffusion coefficient bx,t on the time variable t, and the partial boundary value condition based on a submanifold of ∂Ω×0,T. How to overcome the difficulties arising from the nonstandard growth conditions is another technological novelty of this paper.http://dx.doi.org/10.1155/2020/9397620 |
| spellingShingle | Huashui Zhan On Solutions of a Parabolic Equation with Nonstandard Growth Condition Journal of Function Spaces |
| title | On Solutions of a Parabolic Equation with Nonstandard Growth Condition |
| title_full | On Solutions of a Parabolic Equation with Nonstandard Growth Condition |
| title_fullStr | On Solutions of a Parabolic Equation with Nonstandard Growth Condition |
| title_full_unstemmed | On Solutions of a Parabolic Equation with Nonstandard Growth Condition |
| title_short | On Solutions of a Parabolic Equation with Nonstandard Growth Condition |
| title_sort | on solutions of a parabolic equation with nonstandard growth condition |
| url | http://dx.doi.org/10.1155/2020/9397620 |
| work_keys_str_mv | AT huashuizhan onsolutionsofaparabolicequationwithnonstandardgrowthcondition |