# 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

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topHaslinger, 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

top- G. Duvaut, J. L. Lions, Les inéquations en Mécanique et en Physique, Dunod, Paris, 1972. (1972) Zbl0298.73001MR0464857
- P. D. Panagiotopoulos, Inequality problems in Mechanics and applications. Convex and nonconvex energy functions, Birkhäuser Verlag, Basel/Boston, 1985. (1985) Zbl0579.73014MR0896909
- J. Haslinger, P. D. Panagiotopoulos, The reciprocal variational approach to the Signorini problem with friction. Approximation results, Proc. Royal Soc. of Edinburgh 98 (1984), 250-265. (1984) Zbl0547.73096MR0768357
- P. D. Panagiotopoulos, 10.1007/BF01174652, Acta Mechanica 70 (1987), 145-167. (1987) Zbl0656.73038MR0922344DOI10.1007/BF01174652
- P. D. Panagiotopoulos, P. P. Lazaridis, 10.1016/0020-7683(87)90064-3, Int. J. Solids Struct. 23 (1987), 1465-1484. (1987) Zbl0626.73123MR0918434DOI10.1016/0020-7683(87)90064-3
- P. P. Lazaridis, P. D. Panagiotopoulos, 10.1016/0045-7949(87)90216-1, Соmр. and Structures 25 (1987), 35-49. (1987) Zbl0597.73096MR0880936DOI10.1016/0045-7949(87)90216-1
- I. Hlaváček J. Haslinger J. Nečas, J. Lovíšek, Solution of variational inequalities in Mechanics, Springer Verlag, New York, 1988. (1988) MR0952855
- P. D. Panagiotopoulos, A boundary integral inclusion approach to unilateral B.V.Ps in Elastostatics, Mech. Res. Comn. 10(1983), 91-93. (1983) Zbl0508.73097MR0702788
- J. J. Moreau, La notion de sur-potentiel et les liaisons unilatérales en élastostatique, C. R. Acad. Sc. Paris 267A (1968), 954-957. (1968) Zbl0172.49802MR0241038
- I. Ekeland, R. Temam, Convex Analysis and variational problems, American Elsevier, Amsterodam: North-Holland and New York, 1976. (1976) Zbl0322.90046MR0463994
- F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. (1983) Zbl0582.49001MR0709590
- P. D. Panagiotopoulos, 10.1002/zamm.19850650116, ZAMM 65 (1985), 29-36. (1985) Zbl0574.73015MR0841254DOI10.1002/zamm.19850650116
- K. C. Chang, 10.1016/0022-247X(81)90095-0, J. Math. Anal. Appl. 80 (1981), 102-129. (1981) Zbl0487.49027MR0614246DOI10.1016/0022-247X(81)90095-0
- P. D. Panagiotopoulos, Nonconvex energy functions. Hemivariational inequalities and substationarity principles, Acta Mechanica 42 (1983), 160-183. (1983) Zbl0538.73018MR0715806
- J. J. Moreau P. D. Panagiotopoulos, G. Strang, Topics in Nonsmooth Mechanics, Birkhäuser Verlag, Basel/Boston, 1988. (1988) MR0957086
- J. J. Moreau, P. D. Panagiotopoulos, Topics in Nonsmooth Mechanics and applications, CISM Lecture Notes, Vol. 302, Wien/New York, 1988. (1988) MR0957086
- P. D. Panagiotopoulos, G. Stavroulakis, A variational-hemivariational inequality approach to the laminated plate theory under subdifferential boundary conditions, Quart. Appl. Math. XLVI (19SS), 409-430. (19SS) MR0963579
- J. Haslinger, I. Hlaváček, Convergence of a Finite element method based on the dual Variational Formulation, Apl. Mat. 21 (1976), 43-65. (1976) MR0398126
- J. Nečas, Les methodes directes en teorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
- J. L. Lions, E. Magenes, Problemes aux limites non homogenes, Dunod, Paris, 1968. (1968) Zbl0165.10801
- J. Haslinger I. Hlaváček, Converges of a dual Finite element method in ${R}^{n}$
- F. Brezzi W. Hegerand P. Raviart, Error Estimates for the Finite element solution of Variational Inequalities, Numer. Math. 28 (1979), 431-443. (1979) MR0448949

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