Repositorio de producción científica de la Universidad de Sevilla

Incompressible flow in porous media with fractional diffusion

 

Advanced Search
 
Opened Access Incompressible flow in porous media with fractional diffusion
Cites

Show item statistics
Icon
Export to
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.
Size: 302.5Kb
Format: PDF

URI: http://hdl.handle.net/11441/45190

DOI: 10.1088/0951-7715/22/8/002

See editor´s version

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)