Homogenization of biharmonic equations in domains perforated with tiny holes

Homogenization of the Navier-Stokes Equations in Open Sets Perforated with Tiny Holes I. Abstract Framework, a Volume Distribution of Holes

This paper treats the homogeniza t ion of the Stokes or Navier-Stokes equat ions with a Dirichlet bounda ry condi t ion in a domain conta in ing many t iny solid obstacles, periodically dis tr ibuted in each direction of the axes. (For example, in the three-dimensional case, the obstacles have a size of e a and are located at the nodes of a regular mesh of size e.) A suitable extension of the p...

Homogenization of variational functionals with nonstandard growth in perforated domains

The aim of the paper is to study the asymptotic behavior of solutions to a Neumann boundary value problem for a nonlinear elliptic equation with nonstandard growth condition of the form −div ( |∇u|ε ∇u ) + |u|ε u = f(x) in a perforated domain Ω, ε being a small parameter that characterizes the microscopic length scale of the microstructure. Under the assumption that the functions pε(x) converge...

Homogenization of the Navier-Stokes Equations in Open Sets Perforated with Tiny Holes II: Non-Critical Sizes of the Holes for a Volume Distribution and a Surface Distribution of Holes

This paper is devoted to the homogenizat ion of the Stokes or Navier-Stokes equations with a Dirichlet boundary condit ion in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. For obstacles of critical size it was established in Part I that the limit problem is described by a law of Brinkman type. Here we prove that for smaller obstacles, the...

Homogenization of Hamilton-jacobi Equations in Perforated Sets

Homogenization of a class of elliptic problems with nonlinear boundary conditions in domains with small holes

We consider a class of second order elliptic problems in a domain of RN , N > 2, ε-periodically perforated by holes of size r(ε) , with r(ε)/ε → 0 as ε → 0. A nonlinear Robin-type condition is prescribed on the boundary of some holes while on the boundary of the others as well as on the external boundary of the domain, a Dirichlet condition is imposed. We are interested in the asymptotic behavi...