Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T06:37:14.794Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence of solutions and optimal control problems for hyperbolic hemivariational inequalities

Published online by Cambridge University Press:  17 February 2009

Jong Yeoul Parks  and
Sun Hye Park
Jong Yeoul Parks
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Korea; e-mail: [email protected] and [email protected].
Sun Hye Park
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Korea; e-mail: [email protected] and [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we prove the existence of solutions for hyperbolic hemivariational inequalities and then investigate optimal control problems for some convex cost functionals.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 1 , July 2005 , pp. 51 - 63
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Barbu, V., Analysis and control of nonlinear infinite-dimensional systems (Academic Press, New York, NY, 1993).Google Scholar
[2]Bergounioux, M., “Optimal control of problems governed by abstract elliptic variational inequalities with state constraints”, SIAM J. Control Optim. 36 (1998) 273–289.Google Scholar
[3]Cesari, L., Optimization—theory and applications (Springer, Berlin, 1983).Google Scholar
[4]Duvaut, G. and Lions, J. L., Inequalities in mechanics and physics (Springer, Berlin, 1976).Google Scholar
[5]Ekeland, I. and Temam, R., Convex analysis and variational problems (North-Holland, Amsterdam, 1976).Google Scholar
[6]Haslinger, J. and Panagiotopoulos, P. D., “Optimal control of systems governed by hemivariational inequalities. Existence and approximation results”, Nonlinear Anal. 24 (1995) 105–119.Google Scholar
[7]Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires (Dunod-Gauthier Villars, Paris, 1969).Google Scholar
[8]Lions, J. L., Optimal control of systems governed by partial differential equations (Springer, Berlin, 1971).Google Scholar
[9]Miettinen, M., “A parabolic hemivariational inequality”, Nonlinear Anal. 26 (1996) 725–734.Google Scholar
[10]Miettinen, M. and Panagiotopoulos, P. D., “On parabolic hemivariational inequalities and applications”, Nonlinear Anal. 35 (1999) 885–915.Google Scholar
[11]Migórski, S. and Ochal, A., “Optimal control of parabolic hemivariational inequalities”, J. Global Optim. 17 (2000) 285–300.Google Scholar
[12]Panagiotopoulos, P. D., Inequality problems in mechanics and applications. Convex and nonconvex energy functions (Birkhäuser, Basel, 1985).Google Scholar
[13]Panagiotopoulos, P. D., “Coercive and semicoercive hemivariational inequalities”, Nonlinear Anal. 16 (1991) 209–231.Google Scholar
[14]Panagiotopoulos, P. D., Hemivariational inequalities and applications in mechanics and engineering (Springer, New York, 1993).Google Scholar
[15]Panagiotopoulos, P. D., “Modelling of nonconvex nonsmooth energy problems. Dynamic hemivariational inequalities with impact effects”, J. Comput. Appl. Math. 63 (1995) 123–138.Google Scholar
[16]Park, J. Y., Kim, H. M. and Park, S. H., “On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities”, Nonlinear Anal. 55 (2005) 103–113.Google Scholar
[17]Park, J. Y. and Park, S. H., “Solutions for a hyperbolic system with boundary differential inclusion and nonlinear second-order boundary damping”, Electron. J. Differential Equations, 80 (2005) 1–7.Google Scholar
[18]Rauch, J., “Discontinuous semilinear differential equations and multiple valued maps”, Proc. Amer Math. Soc. 64 (1977) 277–282.Google Scholar
[19]Wang, G., “Optimal control of parabolic differential equations with two point boundary state constraints”, SIAM J. Control Oprim. 38 (2000) 1639–1654.Google Scholar