Solutions of evolutionary equation based on the anisotropic variable exponent Sobolev space

Authors

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

Document Type

Article

Publication Date

6-28-2019

Abstract

In this paper, we are concerned with the equation

ut=∑i=1N∂∂xi(ai(x)|uxi|pi(x)−2uxi)+∑i=1N∂bi(u)∂xi, (x,t)∈Ω×(0,T), where ai(x)|x∈∂Ω=0 and ai(x)|x∈Ω>0 . By the theory of anisotropic variable exponent Sobolev spaces, we study the well-posedness of weak solutions of this equation. Since ai(x) is degenerate on the boundary, the stability of weak solutions may be established without any boundary value condition. The main feature which distinguishes this paper from other related works lies in the fact that we propose a novel analytical method to deal with the stability of weak solutions.

Comments

Copyright © 2019, Springer Nature Switzerland AG

https://rdcu.be/c51v6

Recommended Citation

Zhan, H., Feng, Z. Solutions of evolutionary equation based on the anisotropic variable exponent Sobolev space. Z. Angew. Math. Phys. 70, 110 (2019). https://doi.org/10.1007/s00033-019-1150-y

Publication Title

Z. Angew. Math. Phys.

DOI

10.1007/s00033-019-1150-y