Homogenization and boundary layers

Boundary Layers in the Homogenization of Elliptic Problems

Homogenization and boundary layer

This paper deals with the homogenization of elliptic systems with Dirichlet boundary condition, when the coefficients of both the system and the boundary data are ε-periodic. We show that, as ε → 0, the solutions converge in L2 with a power rate in ε, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the bounda...

Boundary Layers in the Homogenization of a Spectral Problem in Fluid–solid Structures∗

This paper is devoted to the asymptotic analysis of the spectrum of a mathematical model that describes the vibrations of a coupled fluid–solid periodic structure. In a previous work [Arch. Rational Mech. Anal., 135 (1996), pp. 197–257] we proved by means of a Bloch wave homogenization method that, in the limit as the period goes to zero, the spectrum is made of three parts: the macroscopic or ...

Boundary Layers and Heat Transfer on a Rotating Rough Disk

The study of flow and heat transfer over rotating circular disks is of great practical importance in understanding the cooling of rotatory machinery such as turbines, electric motors and design and manufacturing of computer disk drives. This paper presents an analysis of the flow and heat transfer over a heated infinite permeable rough disk. Boundary-layer approximation reduces the elliptic Nav...

Entropy boundary layers

We consider the Euler system of compressible and entropic gaz dynamics in a bounded open domain of R with wall boundary condition. We prove the existence and the stability of families of solutions which correspond to a ground state plus a large entropy boundary layer. The ground state is a solution of the Euler system which satisfies some explicit additional conditions on the boundary. These co...