Solution of boundary value problems in cylinders with a two-layer film inclusion

We consider a class of boundary value problems (elliptic, parabolic and hyperbolic equations) in cylinders, separated by double-layer film on two half cylinder. The film consists of infinitely thin strongly and weakly permeable layers. A theorem of existence and uniqueness. Formulas expressing the solutions to these problems through the solutions of the analogous classical problems in homogeneous cylinders without film are derived.