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2024, Volume 17, Issue 4: 1648-1662. Doi: 10.3934/dcdss.2024008

This issue Previous Article An improved result on bounded/periodic solutions for some scalar delay differential equations Next Article A density result for doubly nonlinear operators in $ L^1 $

Nonnegative weak solutions of anisotropic parabolic equations

Huashui Zhan^1, and
Zhaosheng Feng^2, ,

1.
School of Mathematics and Statistics, Xiamen University of Technology, Xiamen, Fujian 361024, China
2.
School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

^*Corresponding author: Zhaosheng Feng
^*Corresponding author: Zhaosheng Feng

Dedicated to Professor Yihong Du on the Occasion of his 60th Birthday

Received: November 2023

Revised: January 2024

Early access: January 2024

Published: April 2024

The first author is supported by the Natural Science Foundation of Fujian Province (No. 2022J011242), China

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Abstract

In this paper, we consider anisotropic parabolic equations with variable exponents. The existence of weak solution is proved by means of the parabolically regularized method, and the stability of nonnegative solutions is analyzed under certain conditions. By introducing a new kind of weak solution, the stability of the weak solution is established without any boundary value condition.

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Mathematics Subject Classification: Primary: 35K55, 35B35; Secondary: 35K65.

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