Analyse asymptotique en homogénéisation périodique et dans des domaines minces
Renata Bunoiu · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
This synopsis of my work (supporting my request for an authorization to supervise research) surveys my work on asymptotic analysis in periodic homogenization and thin domains. It has two parts. The first part deals with homogenization problems, posed in heterogeneous media with two periodic complementary components. The starting point is the classical problem of diffusion in a heterogeneous periodic medium and the objective is to study the extent of the influence, in the homogenization process, of each hypothesis : the qualitative assumptions on the periodic coefficients which characterize the heterogeneous media, the nonlinear character of the problem and the geometry of the domain in which the problem is posed. The second part deals with the asymptotic analysis of the stationary flow of a Bingham viscoplastic nonlinear fluid. The Bingham fluid, whose constitutive law is nonlinear and has a threshold, is studied in different types of domains, whose geometry is characterized by the presence of asmall parameter. Approximate models that preserve the nonlinear character of the flow are obtained when the small parameter tends to zero. These models reveal new, nonlinear Poiseuille and Darcy laws.