Solutions to polytropic filtration equations with a convection term

Date

2017-09-08

Authors

Zhan, Huashui

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Publisher

Texas State University, Department of Mathematics

Abstract

We introduce a new type of the weak solution of the polytropic filtration equations with a convection term, ut = div(α(x)|u|α|∇u|p-2∇u) + ∂bi(um)/∂xi. Here, Ω ⊂ ℝN is a domain with a C2 smooth boundary ∂Ω, α(x) ∈ C1(Ω̅), p > 1, m = 1 + α/p-1, α > 0, α(x) > 0 when x ∈ Ω and α(x) = 0 when x ∈ ∂Ω. Since the equation is degenerate on the boundary, its weak solutions may lack the needed regularity to have a trace on the boundary. The main aim of the paper is to establish the stability of the weak solution without any boundary value condition.

Description

Keywords

Polytropic filtration equation, Convection term, Stability, Boundary value condition

Citation

Zhan, H. (2017). Solutions to polytropic filtration equations with a convection term. <i>Electronic Journal of Differential Equations, 2017</i>(207), pp. 1-10.

Rights

Attribution 4.0 International

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