Zhuravskaya G. Uniform approximation of solutions of nonlinear problems in perforated domains.

There are considered linear and nonlinear parabolic problems in perforated domain of general structure. In each case the asymptotical expansion of solution and homogenized problem are built and the uniform convergence of the sequence of remainders of the expansion for each case and strong convergence in the space V2 (QT) for nonlinear case are proved. Also there are studied the nonlinear elliptic and parabolic problems in the domains with a fine-grain boundary, when the heterogeneities are inclined near some surface. For the elliptic problem is shown the uniform convergence of the sequence of remainders of the expansion. For the parabolic the strong convergence in the space V2 (QT) and the uniform convergence are proved.