Homogenization of initial boundary value problems for parabolic systems with periodic coefficients

Y.M. Meshkova, T.A. Suslina

Research output

12 Citations (Scopus)

Abstract

© 2015 Taylor & Francis Let (Formula presented.) be a bounded domain of class (Formula presented.). In the Hilbert space (Formula presented.), we consider matrix elliptic second-order differential operators (Formula presented.) and (Formula presented.) with the Dirichlet or Neumann boundary condition on (Formula presented.), respectively. Here (Formula presented.) is the small parameter. The coefficients of the operators are periodic and depend on (Formula presented.). The behaviour of the operator (Formula presented.), (Formula presented.), for small (Formula presented.) is studied. It is shown that, for fixed (Formula presented.), the operator (Formula presented.) converges in the (Formula presented.)-operator norm to (Formula presented.), as (Formula presented.). Here (Formula presented.) is the effective operator with constant coefficients. For the norm of the difference of the operators (Formula presented.) and (Formula presented.), a sharp order estimate (of order (Formula presented.)) is obtained. Also
Original language English 1736-1775 Applicable Analysis 95 8 https://doi.org/10.1080/00036811.2015.1068300 Published - 2016