Averaging of the Dirichlet problem for the spectral hyperbolic quasilinear equation

Abstract

In this paper we establish su cient conditions on the data of the problem which guarantee a convergence of its solution to a limit solution. The domains where we consider the problem has a ne-grained structure.We use S.I.Pohozhaev's method for the proof of the unique solvability in entire and the D.Cioranescu-F.Murat hypothesis for the description of the domain milling.