Solutions to polytropic filtration equations with a convection term
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Date
2017-09-08
Authors
Zhan, Huashui
Journal Title
Journal ISSN
Volume Title
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. Electronic Journal of Differential Equations, 2017(207), pp. 1-10.
Rights
Attribution 4.0 International