Solutions of evolutionary p(x)p(x) -Laplacian equation based on the weighted variable exponent space

Authors

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

Document Type

Article

Publication Date

11-5-2017

Abstract

The paper studies the equation

ut=div(a(x)|∇u|p(x)−2∇u)+∑i=1N∂bi(u)∂xi, (x,t)∈Ω×(0,T), with the boundary degeneracy due to a(x)∣x∈∂Ω=0 , and Ω⊂RN , where N is a positive integer. By the theory of the weighted variable exponent Sobolev spaces, the well posedness of weak solutions of this equation is discussed. The novelty of our results lies in the fact that under certain conditions, if a(x) satisfies ∫Ωa−1p(x)−1dx<∞ , the global stability of weak solutions can be established without any boundary value condition. While ∫Ωa−1p(x)−1dx=∞ , the local stability of weak solutions can be obtained without any boundary value condition.

Comments

Copyright © 2017, Springer International Publishing AG, part of Springer Nature

https://rdcu.be/c51xQ

Recommended Citation

Zhan, H., Feng, Z. Solutions of evolutionary p(x)p(x) -Laplacian equation based on the weighted variable exponent space. Z. Angew. Math. Phys. 68, 134 (2017). https://doi.org/10.1007/s00033-017-0885-6

Publication Title

Z. Angew. Math. Phys.

DOI

10.1007/s00033-017-0885-6