arXiv subjects

Erick Tetsadjio

Publications and source records attributed to Erick Tetsadjio.

3 recordsLinked to original sources

arXiv2026

Homogenization of degenerate parabolic equations with nonlinear Robin reactions in perforated domains

We study periodic homogenization of a parabolic equation with linear, degenerate bulk terms in a perforated domain, with a monotone nonlinear Robin reaction of order $\varepsilon$ on the pore walls. The storage coefficient may vanish on sets of positive measure, and the diagonal diffusion weights are not bounded below but satisfy an inverse-integrability condition. Under positivity of the mean storage, a quantitative cell-detection estimate yields strong compactness of the states and of the scaled traces. The effective equation has positive storage, a positive-definite diffusion matrix given by a weighted cell problem, and a nonlinear volume reaction obtained by averaging over the pore surface. We also prove a strong weighted-gradient corrector and uniform-in-time convergence of the dissipated and stored energies and of the states in the storage-weighted $L^2$ norm.

math.AP↗

arXiv2026

Homogenization of degenerate parabolic Signorini problems with vanishing storage and oscillating surface fluxes

We study the homogenization of a unilateral quasilinear parabolic problem in a periodically perforated medium. The model combines two degeneracies: the coefficient of the time derivative is non-negative and may vanish, while the directional diffusion weights are positive almost everywhere but need not be bounded away from zero. The exterior boundary carries a Signorini condition, and the holes carry an unscaled zero-mean flux oscillating on the diffusive time scale. For any family of microscopic solutions we prove strong space--time $L^2$ compactness through a weighted detection inequality, which replaces the Aubin--Lions lemma when the storage vanishes, and we recover spatial $H^1$ regularity of the limit by a closed-range argument for the weighted two-scale gradients. The limit solves a coupled two-scale problem in Minty form, and microscopic existence holds under joint monotonicity. Under a strengthened condition, the limit decouples into a macroscopic Signorini inequality whose uniqueness follows from an exponential regularization, without time regularity of the limit, and the whole family converges. The surface datum enters both the effective flux and the exterior boundary condition.

math.AP↗

arXiv2017

Reiterated homogenization of hyperbolic-parabolic equations in domains with tiny holes

This article studies the homogenization of hyperbolic-parabolic equations in porous media with tiny holes. We assume that the holes are periodically distributed and that the coefficients of the equations are periodic. Using the multi-scale convergence method, we derive a homogenization result whose limit problem is defined on a fixed domain and is of the same type as the problem with oscillating coefficients.

math.AP↗