Homogenization of initial boundary value problems for parabolic systems with periodic coefficients
Yu. M. Meshkova, Tatiana Aleksandrovna Suslina · Applicable Analysis · 2015
Let be a bounded domain of class . In the Hilbert space , we consider matrix elliptic second-order differential operators and with the Dirichlet or Neumann boundary condition on , respectively. Here is the small parameter. The coefficients of the operators are periodic and depend on . The behaviour of the operator , , for small is studied. It is shown that, for fixed , the operator converges in the -operator norm to , as . Here is the effective operator with constant coefficients. For the norm of the difference of the operators and , a sharp order estimate (of order ) is obtained. Also, we find approximation for the exponential in the -norm with error estimate of order ; in this approximation, a corrector is taken into account. The results are applied to homogenization of solutions of initial boundary value problems for parabolic systems.