Homogenization of a class of nonlinear elliptic equations with nonstandard growth
Brahim Amaziane, S. N. Antont︠s︡ev, Leonid Pankratov · Comptes Rendus Mécanique · 2007
We study the homogenization of the Dirichlet variational problem of a class of nonlinear elliptic equations with nonstandard growth. Such equations arise in many engineering disciplines, such as electrorheological fluids, non-Newtonian fluids with thermo-convective effects, and nonlinear Darcy flow of compressible fluids in heterogeneous porous media. We derive the homogenized model by means of the variational homogenization technique in the framework of Sobolev spaces with variable exponents. This result is then illustrated with a periodic example.