Homogenization Of Global Attractors Of Two Kinds Of Hyperbolic Equations

In this thesis, I have deeply investigated the homogenization of two hyperbolic equations. One is a general quasilinear hyperbolic equation; the other is a semilinear hyperbolic equation with oscillating terms.More specifically, we have studied the following two equations: What we have got for (1) extends the results of D. Cioranescu and P. Donato [2], and our results on (2) extends the results of Bernold Fiedler and Mark I. Vishik[8].Two powerful classical methods in theory of homogenization are De Giorgi's variational convergence method and L. Tartar's energy method. For the homogenization of the partial differential equations with periodical coefficients, in 1989, Nguetseng proposed a new method, i.e., the so-called two-scale convergence method, which exploits fully the periodicity of coefficients. For (1), we have first used the Galerkin method to give the well-posedness, then combined the techniques of the particular choice of the test functions and Tartar's energy method to give the homogenization results. For (2), under some assumptions which allow (2) to have singularities at some points of the domain, we have first given some growth estimates and homogenization estimates, then obtained some estimates on the distance between the attractor of (2) and the attractor of the homogenized equation of (2).