Hubert Nnang

Reiterated homogenization of nonlinear monotone operators in a general deterministic setting

We study reiterated homogenization of a nonlinear non-periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated Σ -convergence. A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ranging from the classical periodicity hypothesis to more complicated, but realistic, structure hypotheses.

Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity

The present work is devoted to the study of homogenization of the weakly damped wave equation ∫Ωρe∂2ue∂t2(t)⋅υdx

Deterministic homogenization of quasilinear damped hyperbolic equations

Abstract Deterministic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term. It is shown by the sigma-convergence method that the sequence of solutions to a class of multi-scale highly oscillatory hyperbolic problems converges to the solution to a homogenized quasilinear hyperbolic problem.

Two-Scale Convergence: Obviousness of the Choice of Test Functions? Not Always

The asymptotic behaviour of a bounded sequence of solutions for some physical problems via the two-scale convergence may not be a direct consequence. In the present example, that is, the homogenization of the weakly damped wave equation (1.1) with initial conditions (1.2), it is shown that the choice of test functions will be more complicated than for the classical homogenization problems.