Existence and stability of the doubly nonlinear anisotropic parabolic equation

Huashui Zhan; Zhaosheng Feng

doi:10.1016/j.jmaa.2020.124850

Existence and stability of the doubly nonlinear anisotropic parabolic equation

J Math Anal Appl. 2021 May 1;497(1):124850. doi: 10.1016/j.jmaa.2020.124850. Epub 2020 Dec 13.

Authors

Huashui Zhan¹, Zhaosheng Feng²

Affiliations

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

Abstract

In this paper, we are concerned with a doubly nonlinear anisotropic parabolic equation, in which the diffusion coefficient and the variable exponent depend on the time variable t. Under certain conditions, the existence of weak solution is proved by applying the parabolically regularized method. Based on a partial boundary value condition, the stability of weak solution is also investigated.

Keywords: Anisotropic parabolic equation; Characteristic function method; Partial boundary value condition; Weak solution.