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Please use this identifier to cite or link to this item: http://dspace.bsu.edu.ru/handle/123456789/20319
Title: A compactness lemma of aubin type and its application to degenerate parabolic equations
Authors: Meirmanov, A. M.
Shmarev, S.
Keywords: mathematics
mathematical analysis
parabolic equations
compactness lemma
two-phase filtration
nonlinear PDE
degenerate parabolic equations
Issue Date: 2015
Citation: Meirmanov, A.M. A compactness lemma of aubin type and its application to degenerate parabolic equations / A. M. Meirmanov, S. Shmarev // Electronic Journal of Differential Equations. - 2015. - Vol.2014, №227.
Abstract: Let Ω ⊂ Rⁿ be a regular domain and Φ(s) ∈ C loc (R) be a given function. If M⊂ L₂ (0, T ; W½ (Ω)) ∩ L ∞ (Ω × (0, T )) is bounded and the set {∂t Φ(v)|v ∈ M} is bounded in L₂ (0, T ; W-¹₂ (Ω)), then there is a sequence {vk} ∈ M such that vk ⇀ v ∈ L₂ (0,T ; W¹₂ (Ω)), and vk → v, Φ(vk) → Φ(v) a.e. in Ωτ = Ω × (0, T). This assertion is applied to prove solvability of the one-dimensional initial and boundary-value problem for a degenerate parabolic equation arising in the Buckley-Leverett model of two-phase filtration. We prove existence and uniqueness of a weak solution, establish the property of finite speed of propagation and construct a self-similar solution
URI: http://dspace.bsu.edu.ru/handle/123456789/20319
Appears in Collections:Статьи из периодических изданий и сборников (на иностранных языках)

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