Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation
We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form d/dt𝒜u+ℬu∋ft in V′, t∈0, T, where V is a real reflexive Banach space, 𝒜 and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′. In view of some practical applications, we assume t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/567241 |
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| author | Ning Su Li Zhang |
| author_facet | Ning Su Li Zhang |
| author_sort | Ning Su |
| collection | DOAJ |
| description | We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form d/dt𝒜u+ℬu∋ft in V′, t∈0, T, where V is a real reflexive Banach space, 𝒜 and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′. In view of some practical applications, we assume that 𝒜 and ℬ are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of 𝒜 and the coerciveness of ℬ. As an application, we give the existence for a nonlinear degenerate parabolic equation. |
| format | Article |
| id | doaj-art-38493dee80d64189a352f44dfaced1b4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-38493dee80d64189a352f44dfaced1b42025-02-03T01:12:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/567241567241Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic EquationNing Su0Li Zhang1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, ChinaDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, ChinaWe consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form d/dt𝒜u+ℬu∋ft in V′, t∈0, T, where V is a real reflexive Banach space, 𝒜 and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′. In view of some practical applications, we assume that 𝒜 and ℬ are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of 𝒜 and the coerciveness of ℬ. As an application, we give the existence for a nonlinear degenerate parabolic equation.http://dx.doi.org/10.1155/2014/567241 |
| spellingShingle | Ning Su Li Zhang Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation Journal of Applied Mathematics |
| title | Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation |
| title_full | Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation |
| title_fullStr | Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation |
| title_full_unstemmed | Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation |
| title_short | Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation |
| title_sort | existence for nonlinear evolution equations and application to degenerate parabolic equation |
| url | http://dx.doi.org/10.1155/2014/567241 |
| work_keys_str_mv | AT ningsu existencefornonlinearevolutionequationsandapplicationtodegenerateparabolicequation AT lizhang existencefornonlinearevolutionequationsandapplicationtodegenerateparabolicequation |