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

Keywords

  • Decay
  • Existence
  • Nonlinear
  • parabolic variational

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Fingerprint Dive into the research topics of 'Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities'. Together they form a unique fingerprint.

  • Cite this