## A boundary multivalued integral ”equation” approach to the semipermeability problem.(English)Zbl 0778.76092

Summary: 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 saddle-point 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. In the last section the theory is illustrated by two numerical examples.

### MSC:

 76S05 Flows in porous media; filtration; seepage 76M30 Variational methods applied to problems in fluid mechanics 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000) 49J40 Variational inequalities
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### References:

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