Yulia Meshkova: On homogenization of periodic hyperbolic systems

Abstract: The talk is devoted to homogenization of solutions of periodic hyperbolic systems with rapidly oscillating coefficients. Classical results in homogenization theory look as the convergence of solutions of the problem with rapidly oscillating coefficients to the solution of the so-called effective problem with constant coefficients. The constants in the corresponding error estimates depend on the differential operator, the lattice of periodicity, and the initial data somehow.

We are interested in the operator error estimates. In such estimates, dependence on the initial data in the error estimates is explicit: we have the norm of the data in the error estimate.
This is extended version of the talk given during the kick-off conference.