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Optimal Shape Design Problems for a Class of Systems Described by Parabolic Hemivariational Inequality

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Abstract

Optimal shape design problems for systems governed by a parabolic hemivariational inequality are considered. A general existence result for this problem is established by the mapping method.

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References

  1. Aubin J. P. and Frankowska H., Set-valued analysis. Birkhäuser, Boston (1990).

    Google Scholar 

  2. Chang K. C., Variational methods for nondifferentiable functionals and applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102–129.

    Google Scholar 

  3. Clarke F. H., Optimization and nonsmooth analysis. John Wiley & Sons, New York (1983).

    Google Scholar 

  4. Duvaut G., Lions J. L., Les inéquations en mécanique et en physique. Dunod, Paris, (1972).

  5. Duvaut G., Lions J. L., Inequalities in mechanics and physics. Springer-Verlag, Berlin, (1976).

    Google Scholar 

  6. Denkowski Z., Migórski S., Optimal shape design for elliptic hemivariational inequalities in nonlinear elasticity, Proc. 12th Conference on Variational Calculus, Optimal Control and Applications. Trassenheide, Germany, September 23-27, 1996 Birkhäuser-Verlag (1997, in press).

  7. Denkowski Z., Migórski S., Optimal shape design problems for a class of systems described by hemivariational inequality, J. Global. Opt. 12 (1998), 37–59.

    Google Scholar 

  8. Gajewski H., Gröger K., Zacharias K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Academie Verlag, Berlin (1974, in Russian).

    Google Scholar 

  9. Haslinger J., Panagiotopoulos P. D., Optimal control of systems governed by hemivariational inequalities: existence and approximation result, Nonlinear Analysis, Theory and Applications. 24, (1995), 105–119.

    Google Scholar 

  10. Lions J. L. Optimal control of systems governed by partial differential equations. Springer Verlag, Berlin (1971).

    Google Scholar 

  11. Lions J. L., Magenes E., Non-homogeneous boundary value problems and applications. Springer Verlag, Berlin (1972).

    Google Scholar 

  12. Liu W. B., Rubio J. E., 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.

    Google Scholar 

  13. Miettinen M., A parabolic hemivariational inequality, Nonlinear Analysis 26 (1996), 725–734.

    Google Scholar 

  14. Miettinen M., Haslinger J., Approximation of optimal control problems of hemivariational inequalities, Numer. Funct. Anal. and Optimiz. 13 (1992), 43–68.

    Google Scholar 

  15. Murat F., Simon J., Sur le controle par un domaine geometrique, Preprint no. 76015, University of Paris 6, (1976) 725–734.

    Google Scholar 

  16. Murat F., Simon J., Etude de problèmes d'optimal design, Proc. 7th IFIP Conference, “Optimization techniques Modelling and Optimization in the Service of Man”, Nice, September 1972, Lect. Notes in Computer Sci. 41, 54–62 (Springer Verlag, 1976).

  17. Naniewicz Z., Panagiotopoulos P. D., Mathematical theory of hemivariational inequalities and applications. Dekker, New York (1995).

    Google Scholar 

  18. Panagiotopoulos P. D., Nonconvex problems of semipermeable media and related topics, Z. Angew. Math. Mech. 65 (1985), 29–36.

    Google Scholar 

  19. Serrin J., On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc. 101 (1961), 139–167.

    Google Scholar 

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Gasiński, L. Optimal Shape Design Problems for a Class of Systems Described by Parabolic Hemivariational Inequality. Journal of Global Optimization 12, 299–317 (1998). https://doi.org/10.1023/A:1008246220601

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