Article
Kyungpook Mathematical Journal 2020; 60(1): 145-161
Published online March 31, 2020
Copyright © Kyungpook Mathematical Journal.
Existence and Behavior Results for a Nonlocal Nonlinear Parabolic Equation with Variable Exponent
Uğur Sert∗, Eylem ÖztÜrk
Department of Mathematics, Hacettepe University, 06800, Beytepe, Ankara, Turkey
e-mail : usert@hacettepe.edu.tr
Department of Mathematics, Hacettepe University, 06800, Beytepe, Ankara, Turkey
e-mail : eozturk@hacettepe.edu.tr
Received: October 12, 2018; Revised: October 4, 2019; Accepted: November 18, 2019
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.
Keywords: degenerate parabolic equations, nonstandard nonlinearity, nonlocal source, solvability theorem, embedding theorems.