Zhan, Huashui2022-06-102022-06-102017-09-08Zhan, H. (2017). Solutions to polytropic filtration equations with a convection term. Electronic Journal of Differential Equations, 2017(207), pp. 1-10.1072-6691https://hdl.handle.net/10877/15901We 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.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalPolytropic filtration equationConvection termStabilityBoundary value conditionArticle