Asymptotic approximations of solutions to parabolic boundary value problems in thin perforated domains of rapidly varying thickness

We consider initial boundary value problems for parabolic differential equations with rapidly oscillating coefficients in thin perforated domains of rapidly varying thickness. Under certain symmetry conditions on the domain and coefficients, we construct an asymptotic expansion of a solution to the problem with homogeneous third kind conditions on the exterior boundary and the boundary of cavities. In the case of inhomogeneous Neumann conditions, we construct an asymptotic solution without symmetry assumptions and prove an asymptotic estimate in the corresponding Sobolev space. Bibliography: 27 titles. Illustrations: 1 figure.