A boundary multivalued integral “equation” approach to the semipermeability problem
Jaroslav Haslinger, Charalampos C. Baniotopoulos, Panagiotis D. Panagiotopoulos · Applications of Mathematics · 1993
The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small number of unknowns. The extension of the present theory to more general nonmonotone semipermeability conditions is also studied. Int the last section the theory is illustrated by two numerical examples.