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Existence and decay of solutions of some nonlinear parabolic variational inequalities

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  • Mitsuhiro Nakao
  • Takashi Narazaki

Abstract

This paper discusses the existence and decay of solutions u ( t ) of the variational inequality of parabolic type: < u ′ ( t ) + A u ( t ) + B u ( t ) − f ( t ) , v ( t ) − u ( t ) > ≧ 0 for ∀ v ∈ L p ( [ 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 .

Suggested Citation

  • Mitsuhiro Nakao & Takashi Narazaki, 1980. "Existence and decay of solutions of some nonlinear parabolic variational inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-24, January.
    • Handle: RePEc:hin:jijmms:307351
    DOI: 10.1155/S0161171280000063
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