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Incompressible flow in porous media with fractional diffusion


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Opened Access Incompressible flow in porous media with fractional diffusion

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Author: Castro Martínez, Ángel
Córdoba Gazolaz, Diego
Gancedo García, Francisco
Orive Illera, Rafael
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2009-08
Published in: Nonlinearity, 22 (8), 1791-1815.
Document type: Article
Abstract: In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove global existence of weak solutions for different cases. Moreover, we obtain the decay of the solution in Lp, for any p ≥ 2, and the asymptotic behavior is shown. Finally, we prove the existence of an attractor in a weak sense and, for the sub-critical dissipative case with α ∈ (1, 2], we obtain the existence of the global attractor for the solutions in the space Hs for any s > (N/2) + 1 − α.
Cite: Castro Martínez, Á., Córdoba Gazolaz, D., Gancedo García, F. y Orive Illera, R. (2009). Incompressible flow in porous media with fractional diffusion. Nonlinearity, 22 (8), 1791-1815.
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DOI: 10.1088/0951-7715/22/8/002

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