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Journal of Optimization Theory and Applications

, Volume 103, Issue 3, pp 567–601 | Cite as

Dynamic Hemivariational Inequalities and Their Applications

  • D. Goeleven
  • M. Miettinen
  • P. D. Panagiotopoulos
Article

Abstract

Dynamic hemivariational inequalities are studied in the present paper. Starting from their solution in the distributional sense, we give certain existence and approximation results by using the Faedo–Galerkin method and certain compactness arguments. Applications from mechanics (viscoelasticity) illustrate the theory.

Hyperbolic hemivariational inequalities dynamic problems nonsmooth nonconvex energy function 

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References

  1. 1.
    Panagiotopoulos, P. D., Nonconvex Energy Functions: Hemivariational Inequalities and Substationarity Principles, Acta Mechanica, Vol. 42, pp. 160–183, 1983.Google Scholar
  2. 2.
    Panagiotopoulos, P. D., Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions, Birkhäuser Verlag, Basel, Switzerland, 1985.Google Scholar
  3. 3.
    Panagiotopoulos, P. D., Coercive and Semicoercive Hemivariational Inequalities, Nonlinear Analysis, Vol. 16, pp. 209–231, 1991.Google Scholar
  4. 4.
    Panagiotopoulos, P. D., Hemivariational Inequalities: Applications in Mechanics and Engineering, Springer Verlag, Berlin, Germany, 1993.Google Scholar
  5. 5.
    Naniewicz, Z., and Panagiotopoulos, P. D., Mathematical Theory of Hemivariational Inequalities and Applications, Marcel Dekker, New York, New York, 1995.Google Scholar
  6. 6.
    Naniewicz, Z., On Some Nonconvex Variational Problems Related to Hemivariational Inequalities, Nonlinear Analysis, Vol. 13, pp. 87–100, 1989.Google Scholar
  7. 7.
    Naniewicz, Z., Hemivariational Inequality Approach to Constrained Problems for Star-Shaped Admissible Sets, Journal of Optimization Theory and Applications, Vol. 83, pp. 97–112, 1994.Google Scholar
  8. 8.
    Goeleven, D., and ThÉra, M., Semicoercive Variational Hemivariational Inequalities, Journal of Global Optimization, Vol. 6, pp. 367–381, 1995.Google Scholar
  9. 9.
    Goeleven, D., On the Hemivariational Inequality Approach to Nonconvex Constrained Problems in the Theory of von Kármán Plates, ZAMM, Vol. 75, pp. 861–866, 1995.Google Scholar
  10. 10.
    Dinca, G., Panagiotopoulos, P. D., and Pop, G., Inégalités Hémi-Variationnelles Semi-Coercives sur des Ensembles Convexes, Comptes Rendus des Séances de l'Académie des Sciences, Série I, Mathématique, Vol. 320, pp. 1183–1186, 1995.Google Scholar
  11. 11.
    Pardalos, P. M., and Panagiotopoulos, P. D., Editors, Nonconvex Energy Functions: Applications in Engineering, Journal of Global Optimization, Vol. 6, pp. 325–449, 1995.Google Scholar
  12. 12.
    Motreanu, D., and Panagiotopoulos, P. D., An Eigenvalue Problem for a Hemivariational Inequality Involving a Nonlinear Compact Operator, Set-Valued Analysis, Vol. 3, pp. 157–166, 1995.Google Scholar
  13. 13.
    Motreanu, D., and Panagiotopoulos, P. D., Nonconvex Energy Functions, Related Eigenvalue Hemivariational Inequalities on the Sphere and Applications, Journal of Global Optimization, Vol. 6, pp. 163–177, 1995.Google Scholar
  14. 14.
    Motreanu, D., and Panagiotopoulos, P. D., A Minimax Approach to the Eigenvalue Problem of Hemivariational Inequalities and Applications, Applicable Analysis, Vol. 58, pp. 53–76, 1995.Google Scholar
  15. 15.
    Panagiotopoulos, P. D., and Haslinger, J., Optimal Control and Identification of Structures Involving Multivalued Nonmonotonicities: Existence and Approximation Results, European Journal of Mechanics, Solids, Vol. 11A, pp. 425–445, 1992.Google Scholar
  16. 16.
    Miettinen, M., Approximation of Hemivariational Inequalities and Optimal Control Problems, Report 59, Department of Mathematics, University of Jyväskylä, 1993.Google Scholar
  17. 17.
    Miettinen, M., and Haslinger, J., Approximation of Nonmonotone Multivalued Differential Inclusions, IMA Journal of Numerical Analysis, Vol. 15, pp. 475–503, 1995.Google Scholar
  18. 18.
    Panagiotopoulos, P. D., Modelling of Nonconvex Nonsmooth Energy Problems: Dynamic Hemivariational Inequalities with Impact Effects, Journal of Computational and Applied Mathematics, Vol. 63, pp. 123–138, 1995.Google Scholar
  19. 19.
    Miettinen, M., A Parabolic Hemivariational Inequality, Nonlinear Analysis, Vol. 26, pp. 725–734, 1996.Google Scholar
  20. 20.
    Carl, S., Enclosure of Solutions for Quasilinear Hemivariational Parabolic Problems, Nonlinear World, Vol. 3, pp. 281–298, 1996.Google Scholar
  21. 21.
    Dautray, R., and Lions, J. L., Analyse Mathématique et Calcul Numérique, Masson, Paris, France, Vol. 8, 1988.Google Scholar
  22. 22.
    Duvaut, G., and Lions, J. L., Les Inéquations en Mécanique et en Physique, Dunod, Paris, France, 1972.Google Scholar
  23. 23.
    Zeidler, E., Nonlinear Functional Analysis and Its Applications, Part 2, Springer Verlag, Berlin, Germany, 1985.Google Scholar
  24. 24.
    Vladimirov, V., Distributions en Physique Mathématique, MIR, Moscow, Russia, 1979.Google Scholar
  25. 25.
    Dunford, N., and Schwartz, J. T., Linear Operators, Part 1: General Theory, Interscience Publishers, New York, New York, 1966.Google Scholar
  26. 26.
    Lions, J. L., Quelques Méthodes de Résolution de Problémes aux Limites non Linéaires, Dunod, Paris, France, 1969.Google Scholar
  27. 27.
    Jarusek, J., Dynamic Contact Problems with Given Friction for Viscoelastic Bodies, Czechoslovak Mathematical Journal, Vol. 46, pp. 475–487, 1996.Google Scholar
  28. 28.
    Lions, J. L., and Magenes, E., Nonhomogenous Boundary-Value Problems and Applications, Springer Verlag, New York, New York, 1972.Google Scholar
  29. 29.
    Panagiotopoulos, P. D., and Koltsakis, E. K., The Nonmonotone Skin Effects in Plane Elasticity Obeying to Linear Elastic and Subdifferential Material Laws, ZAMM, Vol. 70, pp. 13–21, 1990.Google Scholar
  30. 30.
    Moser, K., Faserkunststoffverbund, VDI Verlag, Düsseldorf, Germany, 1992.Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • D. Goeleven
    • 1
  • M. Miettinen
    • 2
  • P. D. Panagiotopoulos
    • 3
    • 4
  1. 1.Institut de Recherche en Mathématiques et Informatique Appliquées, Université de La Réunion, Saint-DenisIle de La RéunionFrance
  2. 2.Department of MathematicsUniversity of JyväskyläJyväskyläFinland
  3. 3.Department of Civil EngineeringAristotle UniversityThessalonikiGreece;
  4. 4.Faculty of Mathematics and PhysicsRWTHAachenGermany

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