Well-posedness problem of an anisotropic parabolic equation

Authors

Huashui Zhan
Zhaosheng Feng, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

1-2020

Abstract

In this paper, we are concerned with well-posedness of an anisotropic parabolic equation with the convection term. When some diffusion coefficients are degenerate on the boundary ∂Ω and the others are positive on ¯¯¯Ω, we propose a novel partial boundary value condition to study the stability of the solutions for the anisotropic parabolic equation. A new concept, the general characteristic function of the domain Ω, is introduced and applied. The existence and stability of the solutions is established under the given partial boundary value conditions.

Comments

http://www.elsevier.com/open-access/userlicense/1.0/

Recommended Citation

Zhan, Huashui, and Zhaosheng Feng. "Well-posedness problem of an anisotropic parabolic equation." Journal of Differential Equations 268, no. 2 (2020): 389-413. https://doi.org/10.1016/j.jde.2019.08.014

Publication Title

Journal of Differential Equations

DOI

10.1016/j.jde.2019.08.014