Existence and decay of solutions of some nonlinear parabolic variational inequalities
This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: <u′(t)+Au(t)+Bu(t)−f(t), v(t)−u(t)>≧0for ∀v∈Lp([0,∞);V)(p≧2) with v(t)∈K a.e. in [0,∞), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlin...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000063 |
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| _version_ | 1832566183336869888 |
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| author | Mitsuhiro Nakao Takashi Narazaki |
| author_facet | Mitsuhiro Nakao Takashi Narazaki |
| author_sort | Mitsuhiro Nakao |
| collection | DOAJ |
| description | This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: <u′(t)+Au(t)+Bu(t)−f(t), v(t)−u(t)>≧0for ∀v∈Lp([0,∞);V)(p≧2) with v(t)∈K a.e. in [0,∞), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as V⊂W⊂H for a Hilbert space H. No monotonicity assumption is made on B. |
| format | Article |
| id | doaj-art-1d7cf6b4d311473e9d118e061195e669 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1d7cf6b4d311473e9d118e061195e6692025-02-03T01:04:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-01317910210.1155/S0161171280000063Existence and decay of solutions of some nonlinear parabolic variational inequalitiesMitsuhiro Nakao0Takashi Narazaki1Department of Mathematics, College of General Education, Kyushu University, Fukuoka, JapanDepartment of Mathematical Sciences, Tokai University, Kanagawa, JapanThis paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: <u′(t)+Au(t)+Bu(t)−f(t), v(t)−u(t)>≧0for ∀v∈Lp([0,∞);V)(p≧2) with v(t)∈K a.e. in [0,∞), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as V⊂W⊂H for a Hilbert space H. No monotonicity assumption is made on B.http://dx.doi.org/10.1155/S0161171280000063existencedecaynonlinear parabolic variational inequalities. |
| spellingShingle | Mitsuhiro Nakao Takashi Narazaki Existence and decay of solutions of some nonlinear parabolic variational inequalities International Journal of Mathematics and Mathematical Sciences existence decay nonlinear parabolic variational inequalities. |
| title | Existence and decay of solutions of some nonlinear parabolic variational inequalities |
| title_full | Existence and decay of solutions of some nonlinear parabolic variational inequalities |
| title_fullStr | Existence and decay of solutions of some nonlinear parabolic variational inequalities |
| title_full_unstemmed | Existence and decay of solutions of some nonlinear parabolic variational inequalities |
| title_short | Existence and decay of solutions of some nonlinear parabolic variational inequalities |
| title_sort | existence and decay of solutions of some nonlinear parabolic variational inequalities |
| topic | existence decay nonlinear parabolic variational inequalities. |
| url | http://dx.doi.org/10.1155/S0161171280000063 |
| work_keys_str_mv | AT mitsuhironakao existenceanddecayofsolutionsofsomenonlinearparabolicvariationalinequalities AT takashinarazaki existenceanddecayofsolutionsofsomenonlinearparabolicvariationalinequalities |