Doubly nonlinear parabolic equations involving variable exponents

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8 Citations (Scopus)

Abstract

This paper is concerned with doubly nonlinear parabolic equations involving variable exponents. The existence of solutions is proved by developing an abstract theory on doubly nonlinear evolution equations governed by gradient operators. In contrast to constant exponent cases, two nonlinear terms have inhomogeneous growth and some difficulty may occur in establishing energy estimates. Our method of proof relies on an efficient use of Legendre-Fenchel transforms of convex functionals and an energy method.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume7
Issue number1
DOIs
Publication statusPublished - 2014 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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