| Title:
|
A boundary multivalued integral “equation” approach to the semipermeability problem (English) |
| Author:
|
Haslinger, Jaroslav |
| Author:
|
Baniotopoulos, C. C. |
| Author:
|
Panagiotopoulos, Panagiotis D. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
39-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 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. (English) |
| Keyword:
|
approximations of unilateral BVP |
| Keyword:
|
mixed and dual variational formulation of unilateral BVP |
| Keyword:
|
semipermeable membrane |
| Keyword:
|
infinite thickness |
| Keyword:
|
convex superpotentials |
| Keyword:
|
saddle-point technique |
| Keyword:
|
boundary minimization problem |
| MSC:
|
35J85 |
| MSC:
|
35R35 |
| MSC:
|
49J40 |
| MSC:
|
65N30 |
| MSC:
|
76M30 |
| MSC:
|
76M99 |
| MSC:
|
76S05 |
| idZBL:
|
Zbl 0778.76092 |
| idMR:
|
MR1202079 |
| DOI:
|
10.21136/AM.1993.104533 |
| . |
| Date available:
|
2008-05-20T18:44:55Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104533 |
| . |
| Reference:
|
[1] G. Duvaut, J. L. Lions: Les inéquations en Mécanique et en Physique.Dunod, Paris, 1972. Zbl 0298.73001, MR 0464857 |
| Reference:
|
[2] P. D. Panagiotopoulos: Inequality problems in Mechanics and applications. Convex and nonconvex energy functions.Birkhäuser Verlag, Basel/Boston, 1985. Zbl 0579.73014, MR 0896909 |
| Reference:
|
[3] 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. Zbl 0547.73096, MR 0768357 |
| Reference:
|
[4] P. D. Panagiotopoulos: Multivalued boundary integral equations for inequality problems. The convex case.Acta Mechanica 70 (1987), 145-167. Zbl 0656.73038, MR 0922344, 10.1007/BF01174652 |
| Reference:
|
[5] P. D. Panagiotopoulos, P. P. Lazaridis: Boundary minimum principles for the unilateral contact problems.Int. J. Solids Struct. 23 (1987), 1465-1484. Zbl 0626.73123, MR 0918434, 10.1016/0020-7683(87)90064-3 |
| Reference:
|
[6] P. P. Lazaridis, P. D. Panagiotopoulos: Boundary variational "principles" for inequality Structural Analysis problems and numerical applications.Соmр. and Structures 25 (1987), 35-49. Zbl 0597.73096, MR 0880936, 10.1016/0045-7949(87)90216-1 |
| Reference:
|
[7] I. Hlaváček J. Haslinger J. Nečas, J. Lovíšek: Solution of variational inequalities in Mechanics.Springer Verlag, New York, 1988. MR 0952855 |
| Reference:
|
[8] P. D. Panagiotopoulos: A boundary integral inclusion approach to unilateral B.V.Ps in Elastostatics.Mech. Res. Comn. 10(1983), 91-93. Zbl 0508.73097, MR 0702788 |
| Reference:
|
[9] J. J. Moreau: La notion de sur-potentiel et les liaisons unilatérales en élastostatique.C. R. Acad. Sc. Paris 267A (1968), 954-957. Zbl 0172.49802, MR 0241038 |
| Reference:
|
[10] I. Ekeland, R. Temam: Convex Analysis and variational problems.American Elsevier, Amsterodam: North-Holland and New York, 1976. Zbl 0322.90046, MR 0463994 |
| Reference:
|
[11] F. H. Clarke: Optimization and Nonsmooth Analysis.Wiley, New York, 1983. Zbl 0582.49001, MR 0709590 |
| Reference:
|
[12] P. D. Panagiotopoulos: Nonconvex problems of semipermeable media and related topics.ZAMM 65 (1985), 29-36. Zbl 0574.73015, MR 0841254, 10.1002/zamm.19850650116 |
| Reference:
|
[13] K. C. Chang: Variational methods for non-differentiable functionals and their applications to partial differential equations.J. Math. Anal. Appl. 80 (1981), 102-129. Zbl 0487.49027, MR 0614246, 10.1016/0022-247X(81)90095-0 |
| Reference:
|
[14] P. D. Panagiotopoulos: Nonconvex energy functions. Hemivariational inequalities and substationarity principles.Acta Mechanica 42 (1983), 160-183. Zbl 0538.73018, MR 0715806 |
| Reference:
|
[15] J. J. Moreau P. D. Panagiotopoulos, G. Strang: Topics in Nonsmooth Mechanics.Birkhäuser Verlag, Basel/Boston, 1988. MR 0957086 |
| Reference:
|
[16] J. J. Moreau, P. D. Panagiotopoulos: Topics in Nonsmooth Mechanics and applications.CISM Lecture Notes, Vol. 302, Wien/New York, 1988. MR 0957086 |
| Reference:
|
[17] 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. MR 0963579 |
| Reference:
|
[18] J. Haslinger, I. Hlaváček: Convergence of a Finite element method based on the dual Variational Formulation.Apl. Mat. 21 (1976), 43-65. MR 0398126 |
| Reference:
|
[19] J. Nečas: Les methodes directes en teorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[20] J. L. Lions, E. Magenes: Problemes aux limites non homogenes.Dunod, Paris, 1968. Zbl 0165.10801 |
| Reference:
|
[21] J. Haslinger I. Hlaváček: Converges of a dual Finite element method in $R^n$. |
| Reference:
|
[22] F. Brezzi W. Hegerand P. Raviart: Error Estimates for the Finite element solution of Variational Inequalities.Numer. Math. 28 (1979), 431-443. MR 0448949 |
| . |
