Homogenization of a quasilinear parabolic equation with vanishing viscosity

We study the limit as epsilon --> 0 of the solutions of the equation partial derivative(t)u(epsilon) + div(x)[A(x/epsilon, u(epsilon))],- epsilon Delta(x)u(epsilon) = 0. After computing the homogenized problem thanks to formal double-scale expansions, we prove that as epsilon goes to 0, u(epsilon) behaves in L-loc(2) as v(x/epsilon, (u) over bar (t, x)), to where v is determined by a cell problem and (u) over bar is the solution of the homogenized problem. The proof relies on the use of two-scale Young measures, a generalization of Young measures adapted to two-scale homogenization problems. (C) 2006 Elsevier SAS. All rights reserved.