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Dive into the research topics where Rafael Orive is active.

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Featured researches published by Rafael Orive.


Siam Journal on Mathematical Analysis | 2002

BLOCH APPROXIMATION IN HOMOGENIZATION AND APPLICATIONS

Carlos Conca; Rafael Orive; Muthusamy Vanninathan

The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions


Nonlinearity | 2009

Incompressible flow in porous media with fractional diffusion

Angel de Castro; Diego Córdoba; Francisco Gancedo; Rafael Orive

u^\varepsilon


Mathematical Models and Methods in Applied Sciences | 2001

Asymptotic expansion for damped wave equations with periodic coefficients

Rafael Orive; Enrique Zuazua; A. F. Pazoto

of boundary value problems associated with such operators when the period


Journal of Mathematical Physics | 2007

Analytical behavior of two-dimensional incompressible flow in porous media

Diego Córdoba; Francisco Gancedo; Rafael Orive

\varepsilon>0


Journal of Mathematical Physics | 2006

On Burnett coefficients in periodic media

Carlos Conca; Rafael Orive; M. Vanninathan

of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as


Pure and Applied Geophysics | 2015

Introduction to Mathematics and Geosciences: Global and Local Perspectives, Volume I

Rafael Orive; María Luisa Osete; Jesús Ildefonso Díaz Díaz; José Fernández

\varepsilon\to 0


Multiscale Modeling & Simulation | 2005

FINITE DIFFERENCE APPROXIMATION OF HOMOGENIZATION PROBLEMS FOR ELLIPTIC EQUATIONS

Rafael Orive; Enrique Zuazua

towards the homogenized solution was furnished using Bloch wave decomposition.Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution


Archive | 2007

Analytical behaviour of 2D incompressible flow in porous media

Diego Córdoba; Francisco Gancedo; Rafael Orive

u^\varepsilon


Asymptotic Analysis | 2009

Bloch waves homogenization of a Dirichlet problem in a periodically perforated domain

Delphine Dupuy; Rafael Orive; Loredana Smaranda

. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to captur...


Glasgow Mathematical Journal | 2009

THE BEST SOBOLEV TRACE CONSTANT IN PERIODIC MEDIA FOR CRITICAL AND SUBCRITICAL EXPONENTS

Julián Fernández Bonder; Rafael Orive; Julio D. Rossi

In this paper we study heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcys law. We show the formation of singularities with infinite energy, and for infinite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove the 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 behaviour is shown. Finally, we prove the existence of an attractor in a weak sense and, for the sub-critical dissipative case with ? (1, 2], we obtain the existence of the global attractor for the solutions in the space Hs for any s > (N/2) + 1 ? ?.

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Diego Córdoba

Spanish National Research Council

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Enrique Zuazua

Autonomous University of Madrid

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M. Vanninathan

Tata Institute of Fundamental Research

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Julio D. Rossi

University of Buenos Aires

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Angel de Castro

Autonomous University of Madrid

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