Existence and Behavior Results for a Nonlocal Nonlinear Parabolic Equation with Variable Exponent


SERT U., ÖZTÜRK E.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.60, no.1, pp.145-161, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.5666/kmj.2020.60.1.145
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index, Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.145-161

Abstract

In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.