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

Jingfeng Shao; Zhichang Guo; Zhongxiang Zhou

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

Analysis of PDEs 2024-04-24 v1

Authors: Jingfeng Shao , Zhichang Guo , Zhongxiang Zhou

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.

Keywords

weak solution parabolic equation variable exponent existence support non-expansion

Cite

@article{arxiv.2404.14918,
  title  = {Existence of weak solutions for a class of non-divergent parabolic equations with variable exponent},
  author = {Jingfeng Shao and Zhichang Guo and Zhongxiang Zhou},
  journal= {arXiv preprint arXiv:2404.14918},
  year   = {2024}
}

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