Existence of weak solutions for a class of non-divergent parabolic equations with variable exponent

Jingfeng Shao; Zhichang Guo; Zhongxiang Zhou

paper

Existence of weak solutions for a class of non-divergent parabolic equations with variable exponent

arXiv:2404.14918

Abstract

A doubly degenerate parabolic equation in non-divergent form with variable growth is investigated in this paper. In suitable spaces, we prove the existence of weak solutions of the equation for cases $1 \leq m < 2$ and $m \geq 2$ in different ways. And we establish the non-expansion of support of the solution for the problem.