High-order mixed-type differential equations with weighted integral boundary conditions.
Hölder estimates and hypoellipticity
The aim of this paper is to show how, in order to prove regularity theorems, Hölder estimates, i.e. estimates involving products of powers of different semi-norms, can be used as well as standard estimates, and may in some instances be casier to prove.
Hölder estimates for nonlinear degenerate parabolic sytems.
Hölder-continuous solution for a nonlinear elasticity system.
Homogénéisation et compacité par compensation
Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
Homogenization of a three-phase composites of double-porosity type
In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size ( and ) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of the same order (the so-called double-porosity type scaling) while the matrix material has a conductivity of...
Hypoellipticité analytique pour des opérateurs à caractéristiques multiples - Démonstration élémentaire
Hysteresis and Periodic Solutions of Semilinear and Quasilinear Wave Equations.