Artículo
Incompressible flow in porous media with fractional diffusion
Autor/es | Castro Martínez, Ángel
Córdoba Gazolaz, Diego Gancedo García, Francisco Orive Illera, Rafael |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2009-08 |
Fecha de depósito | 2016-09-21 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | MTM2005-05980
S-0505/ESP/0158 MTM2005-00714 |
Cita | 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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