Youcef Amirat

Asymptotic Approximation of the Solution of the Laplace Equation in a Domain with Highly Oscillating Boundary

We study the asymptotic behavior of the solution of the Laplace equation in a domain, a part of whose boundary is highly oscillating. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a wall and at the top by a rugose wall. The latter is a plane covered with periodic asperities whose size depends on a small parameter,

MATHEMATICAL ANALYSIS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT MODELS IN POROUS MEDIA

\varepsilon >0.

Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux

The assumption of sharp asperities is made; that is, the height of the asperities is fixed. Using a boundary layer corrector, we derive and analyze a nonoscillating approximation of the solution at order

Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues

{\cal O}(\varepsilon^{3/2})

Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary

for the H1 -norm.

Some results on homogenization of convection-diffusion equations

We discuss a three-dimensional displacement model of one miscible compressible fluid by another in a porous medium. The motion is modeled by a nonlinear system of parabolic type coupling the pressure and the concentration. We give an existence result of weak solutions for a model with diffusion and dispersion, using the Schauder fixed point theorem. We also study a model in the absence of diffusion and dispersion. The system becomes of parabolic-hyperbolic type, the existence of global weak solutions is then obtained through a compensated compactness argument.

ASYMPTOTIC BEHAVIOR OF THE INDUCTANCE COEFFICIENT FOR THIN CONDUCTORS

Resume On s’interesse a l’homogeneisation de l’equation hyperbolique modele ∂ t u e + a e ( t , y ) ∂ x u e = 0 , t > 0 , x ∈ ℝ , y ∈ Ω ⊂ ℝ N , munie d’une condition initiale (et d’une condition aux limites lorsque x ∈]0, 1[). Pour cela, nous caracterisons la limite L∞(Ω) faible * de fonctions du type φ x e ( λ ) = ( λ − A e ( y ) ) − 1 definies pour , λ ∉ [m, M] et verifiant 0

Analysis of a one-dimensional model for compressible miscible displacement in porous media

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics.

Homogénéisation d'un modèle d'écoulements miscibles en milieu poreux

We study the asymptotic behaviour of the solution of Laplace equation in a domain with very rapidly oscillating boundary. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rugose wall. The rugose wall is a plane covered with periodic asperities which size depends on a small parameter ε > 0. The assumption of sharp asperities is made, that is the height of the asperities does not vanish as ε → 0. We prove that, up to an exponentially decreasing error, the solution of Laplace equation can be approximated, outside a layer of width 2ε, by a non-oscillating explicit function.

Global Weak Solutions to Equations of Compressible Miscible Flows in Porous Media

We consider some models of degenerate convection-diffusion equations with oscillating coefficients. We prove that the homogenization process produces non-local and memory effects when the diffusion is longitudinal. When the diffusion is transverse we obtain a stability result. We also examine parametrized families of diffusion equations involving non-local terms.