Download PDF - An optimal shape design problem for a hyperbolic hemivariational inequalityAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

An optimal shape design problem for a hyperbolic hemivariational inequality

Authors 1

Affiliations

  1. Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 Cracow, Poland

Abstract

In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.

Keywords

ENG
optimal shape design, mapping method, hemivariational inequalities, Clarke subdifferential

Bibliography

  1. W. Bian, Existence Results for Second Order Nonlinear Evolution Inclusions, Indian J. Pure Appl. Math. 29 (11) (1998), 1177-1193.
  2. F.E. Browder and P. Hess, Nonlinear Mappings of Monotone Type in Banach Spaces, J. of Funct. Anal. 11 (1972), 251-294.
  3. K.C. Chang, Variational methods for nondifferentiable functionals and applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
  4. F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York 1983.
  5. Z. Denkowski and S. Migórski, Optimal Shape Design Problems for a Class of Systems Described by Hemivariational Inequality, J. Global. Opt. 12 (1998), 37-59.
  6. L. Gasiński, Optimal Shape Design Problems for a Class of Systems Described by Parabolic Hemivariational Inequality, J. Global. Opt. 12 (1998), 299-317.
  7. L. Gasiński, Hyperbolic Hemivariational Inequalities, in preparation.
  8. W.B. Liu and J.E. Rubio, Optimal Shape Design for Systems Governed by Variational Inequalities, Part 1: Existence Theory for the Elliptic Case, Part 2: Existence Theory for Evolution Case, J. Optim. Th. Appl. 69 (1991), 351-371, 373-396.
  9. A.M. Micheletti, Metrica per famiglie di domini limitati e proprieta generiche degli autovalori, Annali della Scuola Normale Superiore di Pisa 28 (1972), 683-693.
  10. J.J. Moreau, Le Notions de Sur-potential et les Liaisons Unilatérales en Élastostatique, C.R. Acad. Sc. Paris 267A (1968), 954-957.
  11. J.J. Moreau, P.D. Panagiotopoulos and G. Strang, Topics in Nonsmooth Mechanics, Birkhäuser, Basel 1988.
  12. F. Murat and J. Simon, Sur le Controle par un Domaine Geometrique, Preprint no. 76015, University of Paris 6 (1976), 725-734.
  13. Z. Naniewicz and P.D. Panagiotopoulos, Mathematical Theory of Hemivariational Inequalities and Applications, Dekker, New York 1995.
  14. P.D. Panagiotopoulos, Nonconvex Superpotentials in the Sense of F.H. Clarke and Applications, Mech. Res. Comm. 8 (1981), 335-340.
  15. P.D. Panagiotopoulos, Nonconvex problems of semipermeable media and related topics, Z. Angew. Math. Mech. 65 (1985), 29-36.
  16. P.D. Panagiotopoulos, Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions, Birkhäuser, Basel 1985.
  17. O. Pironneau, Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York 1984.
  18. J. Sokołowski and J.P. Zolesio, Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer Verlag 1992.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2000/20/1
Export to PBN, Opens in new tab
Pages:
41-50
Main language of publication
English
Published
2000

DOI: 10.7151/dmgt.1003

Exact and natural sciences