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...

Full description

Saved in:
Bibliographic Details
Main Authors: Mitsuhiro Nakao, Takashi Narazaki
Format: Article
Language:English
Published: Wiley 1980-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171280000063
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832566183336869888
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