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arXiv · 2404.14918

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

Jingfeng Shao·Zhichang Guo·Zhongxiang Zhou
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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.

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Jingfeng Shao, Zhichang Guo, Zhongxiang Zhou. 2024-04-23. Existence of weak solutions for a class of non-divergent parabolic equations with variable exponent. https://arxiv.org/abs/2404.14918

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