Existence of extremal periodic solutions for quasilinear parabolic equations
In this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools u...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | Abstract and Applied Analysis |
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| Online Access: | http://dx.doi.org/10.1155/S1085337597000389 |
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| _version_ | 1832550322256478208 |
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| author | Siegfried Carl |
| author_facet | Siegfried Carl |
| author_sort | Siegfried Carl |
| collection | DOAJ |
| description | In this paper we consider a quasilinear parabolic equation in a
bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction. |
| format | Article |
| id | doaj-art-01de9b620bec46969e6f5d253414a456 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-01de9b620bec46969e6f5d253414a4562025-02-03T06:07:04ZengWileyAbstract and Applied Analysis1085-33751997-01-0123-425727010.1155/S1085337597000389Existence of extremal periodic solutions for quasilinear parabolic equationsSiegfried Carl0Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, Institut für Analysis, Halle D-06099, GermanyIn this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.http://dx.doi.org/10.1155/S1085337597000389Quasilinear parabolic equationsDirichlet-periodic boundary conditionsextremal solutionsupper and lower solutionspseudomonotone operatorstruncation and comparison techniques. |
| spellingShingle | Siegfried Carl Existence of extremal periodic solutions for quasilinear parabolic equations Abstract and Applied Analysis Quasilinear parabolic equations Dirichlet-periodic boundary conditions extremal solutions upper and lower solutions pseudomonotone operators truncation and comparison techniques. |
| title | Existence of extremal periodic solutions for quasilinear parabolic equations |
| title_full | Existence of extremal periodic solutions for quasilinear parabolic equations |
| title_fullStr | Existence of extremal periodic solutions for quasilinear parabolic equations |
| title_full_unstemmed | Existence of extremal periodic solutions for quasilinear parabolic equations |
| title_short | Existence of extremal periodic solutions for quasilinear parabolic equations |
| title_sort | existence of extremal periodic solutions for quasilinear parabolic equations |
| topic | Quasilinear parabolic equations Dirichlet-periodic boundary conditions extremal solutions upper and lower solutions pseudomonotone operators truncation and comparison techniques. |
| url | http://dx.doi.org/10.1155/S1085337597000389 |
| work_keys_str_mv | AT siegfriedcarl existenceofextremalperiodicsolutionsforquasilinearparabolicequations |