Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities

Mitsuhiro Nakao, Takashi Narazaki

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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)> ≧ 0 for ∀ 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.

Original languageEnglish
Pages (from-to)79-102
Number of pages24
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume3
Issue number1
DOIs
Publication statusPublished - 1980
Externally publishedYes

Fingerprint

Parabolic Variational Inequalities
Decay of Solutions
Nonlinear Operator
Existence of Solutions
Uniformly Convex Banach Space
Monotone Operator
Closed set
Convex Sets
Variational Inequalities
Monotonicity
Hilbert space
Banach space

Keywords

  • Decay
  • Existence
  • Nonlinear
  • parabolic variational

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities. / Nakao, Mitsuhiro; Narazaki, Takashi.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 3, No. 1, 1980, p. 79-102.

Research output: Contribution to journalArticle

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