Anvarbek Meirmanov, Sergey Shmarev
Let be a regular domain and be a given function. If is bounded and the set is bounded in , then there is a sequence such that , and , a.e. in . 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.
Submitted September 25, 2014. Published October 27, 2014.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Compactness lemma; two-phase filtration; nonlinear PDE; degenerate parabolic equations.
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| Anvarbek Meirmanov |
Department of mahtematics, Belgorod State University
ul.Pobedi 85, 308015 Belgorod, Russia
| Sergey Shmarev |
Department of Mathematics, University of Oviedo
c/Calvo Sotelo s/n, 33007, Oviedo, Spain
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