Degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities

Mariya Ptashnyk (Lead / Corresponding author)

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

The existence of solutions of degenerate quasilinear pseudoparabolic equations, where the term ∂t u is replace by ∂t b (u), with memory terms and quasilinear variational inequalities is shown. The existence of solutions of equations is proved under the assumption that the nonlinear function b is monotone and a gradient of a convex, continuously differentiable function. The uniqueness is proved for Lipschitz-continuous elliptic parts. The existence of solutions of quasilinear variational inequalities is proved under stronger assumptions, namely, the nonlinear function defining the elliptic part is assumed to be a gradient and the function b to be Lipschitz continuous.

Original languageEnglish
Pages (from-to)2653-2675
Number of pages23
JournalNonlinear Analysis
Volume66
Issue number12
DOIs
Publication statusPublished - 15 Jun 2007

Keywords

  • Degenerate parabolic equations
  • Equations with memory terms
  • Pseudoparabolic equations

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