A boundary multivalued integral “equation” approach to the semipermeability problem

Jaroslav Haslinger; Charalambos C. Baniotopoulos; Panagiotis D. Panagiotopoulos

Applications of Mathematics (1993)

  • Volume: 38, Issue: 1, page 39-60
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Haslinger, Jaroslav, Baniotopoulos, Charalambos C., and Panagiotopoulos, Panagiotis D.. "A boundary multivalued integral “equation” approach to the semipermeability problem." Applications of Mathematics 38.1 (1993): 39-60. <http://eudml.org/doc/15735>.

@article{Haslinger1993,
abstract = {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.},
author = {Haslinger, Jaroslav, Baniotopoulos, Charalambos C., Panagiotopoulos, Panagiotis D.},
journal = {Applications of Mathematics},
keywords = {approximations of unilateral BVP; mixed and dual variational formulation of unilateral BVP; semipermeable membrane; infinite thickness; convex superpotentials; saddle-point technique; boundary minimization problem; mixed and dual variational formulation; semipermeable membrane; infinite thickness; convex superpotentials; saddle-point technique; boundary minimization problem},
language = {eng},
number = {1},
pages = {39-60},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A boundary multivalued integral “equation” approach to the semipermeability problem},
url = {http://eudml.org/doc/15735},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Baniotopoulos, Charalambos C.
AU - Panagiotopoulos, Panagiotis D.
TI - A boundary multivalued integral “equation” approach to the semipermeability problem
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 1
SP - 39
EP - 60
AB - 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.
LA - eng
KW - approximations of unilateral BVP; mixed and dual variational formulation of unilateral BVP; semipermeable membrane; infinite thickness; convex superpotentials; saddle-point technique; boundary minimization problem; mixed and dual variational formulation; semipermeable membrane; infinite thickness; convex superpotentials; saddle-point technique; boundary minimization problem
UR - http://eudml.org/doc/15735
ER -

References

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