Stability of weak solutions of a non-Newtonian polytropic filtration equation

Date

2018-11-26

Authors

Zhan, Huashui
Feng, Zhaosheng

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We study a non-Newtonian polytropic filtration equation with a convection term. We introduce new type of weak solutions and show the existence of weak solutions. We show that when ∫Ω [α(x)] -1(p-1) dx < ∞, the stability of weak solutions is based on the usual initial-boundary value conditions. When 1 < p < 2, under the given conditions on the diffusion coefficient and the convection term, the stability of weak solutions can be proved without any boundary value condition. In particular, the stability results are presented based on the given optimal boundary value condition.

Description

Keywords

Weak solution, Convection term, Stability, Boundary value condition

Citation

Zhan, H., & Feng, Z. (2018). Stability of weak solutions of a non-Newtonian polytropic filtration equation. <i>Electronic Journal of Differential Equations, 2018</i>(190), pp. 1-18.

Rights

Attribution 4.0 International

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