Solution of boundary value problems in cylinders separated by a three-layer film into two semicylinders

Abstract

Boundary value problems are considered for the class of equations ∂x2u + L[u] = 0 in cylinders D = (x ∈ R, y ∈ Q ⊆ Rm) with an infinitely thin film at x = 0 consisting of three sublayers with alternating high and low permeability (L-linear differential operator with respect to yi). The solutions of the problems are expressed in terms of those of the corresponding classical boundary value problems in homogeneous cylinders D with no film. The resulting formulas have the form of simple quadrature rules, which are amenable to numerical computations.