ABSTRACT
Let be a bounded domain of class . In , we consider a self-adjoint matrix strongly elliptic second-order differential operator , , with the Dirichlet boundary condition. The coefficients of the operator are periodic and depend on . We are interested in the behavior of the operators and , , in the small period limit. For these operators, approximations in the norm of operators acting from a certain subspace of the Sobolev space to are found. Moreover, for , the approximation with the corrector in the norm of operators acting from to is obtained. The results are applied to homogenization for the solution of the first initial-boundary value problem for the hyperbolic equation .
Acknowledgments
The author is deeply grateful to T. A. Suslina for her attention to this work.
Disclosure statement
No potential conflict of interest was reported by the author.