Approximations of effective coefficients in stochastic homogenization
Homogenization of a singular random one-dimensional PDE
This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.
Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions
The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and -growth assumptions on the bulk energy, and the assumption that the surface energy satisfies -growth upper bound,...
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( = < 1), or is much greater than ( = > 1). We consider all three cases.
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( = < 1), or is much greater than ( = ...
Homogenization in perforated domains with rapidly pulsing perforations
The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates of the...
Homogenization in perforated domains with rapidly pulsing perforations
The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get estimates of the solutions....
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