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.