Global Weak Solutions for a Parabolic System Modeling a One-Dimensional Miscible Flow in Porous Media |
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Authors: | Youcef Amirat Abdelhamid Ziani |
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Institution: | aLaboratoire de Mathématiques Appliquées, CNRS UMR 6620, Université Blaise Pascal, 63177, Aubière, Cedex, France;bDépartement de Mathématiques, Université de Nantes, BP 92208, 44322, Nantes Cedex 3, France |
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Abstract: | We consider an initial boundary value problem for a nonlinear differential system of two equations. Such a system is formed by the equations of compressible miscible flow in a one-dimensional porous medium. No assumption about the mobility ratio is involved. Under some reasonable assumptions on the data, we prove the existence of a global weak solution. Our basic approach is the semi-Galerkin method. We use the technique of renormalized solutions for parabolic equations in the derivation ofa prioriestimates. |
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