Existence and Behavior Results For a Nonlocal Nonlinear Parabolic Equation With Variable Exponent

TL;DR

This paper investigates the existence and behavior of solutions for a nonlocal nonlinear parabolic equation with variable exponents, extending previous results to more general conditions and analyzing solution properties in the homogeneous case.

Contribution

It establishes the existence of weak solutions under broader conditions and explores solution behavior for the homogeneous problem.

Findings

Existence of weak solutions under general conditions

Behavior analysis of solutions in the homogeneous case

Extension of solvability results to nonlocal, variable exponent equations

Abstract

In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general conditions. In addition, we obtain some results on the behavior of the solution when the problem is homogeneous.