Existence of solutions for second order evolution inclusions with application to mechanical contact problems

Optimization

Volumn 55, Issue 1-2, 2006, Pages 101-120

  Migórski, StanisŁaw ^a   Ochal, Anna ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Contact problem; Friction; Hemivariational inequality; Pseudomonotone; Subdifferential; Viscoelasticity

Indexed keywords

EID: 33646448423     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331930500530187     Document Type: Article

References (28)

1. Ahmed, N.U., 1986, Existence of optimal controls for a class of systems governed by differential inclusions in Banach spaces. Journal of Optimization Theory and Applications, 50(2), 213-237.
2. Ahmed, N.U., 1994, In: Pavel, N.H. (Ed.) Optimal Relaxed Controls for Nonlinear Infinite Dimensional Stochastic Differential Inclusions, Lecture Notes in Pure and Applied Mathematics, Vol. 160 (New York, Basel, Hong Kong: Marcel Dekker, Inc.), 1-19.
3. Ahmed, N.U. and Kerbal, S., 1993, Optimal control of nonlinear second order evolution equations. Journal of Applied Mathematics and Stochastic Analysis, 6, 123-136.
4. Aubin, J.P. and Cellina, A., 1984, Differential Inclusions. Set-Valued Maps and Viability Theory (Berlin, New York, Tokyo: Springer-Verlag).
5. Clarke, F.H., 1983, Optimization and Nonsmooth Analysis (New York: Wiley-Interscience).
6. Denkowski, Z., Migórski, S. and Papageorgiou, N.S., 2003, An Introduction to Nonlinear Analysis: Theory (Boston, Dordrecht, London, New York: Kluwer Academic/Plenum Publishers).
7. Denkowski, Z., Migórski, S. and Papageorgiou, N.S., 2003, An Introduction to Nonlinear Analysis: Applications (Boston, Dordrecht, London, New York: Kluwer Academic/Plenum Publishers).
8. Dumont, Y., Goeleven, D., Rochdi, M., Kuttler, K.L. and Shillor, M., 2000, A dynamic model with friction and adhesion with applications to rocks. Journal of Mathematical Analysis and Applications, 247, 87-109.
9. Duvaut, G. and Lions, J.L., 1976, Inequalities in Mechanics and Physics (Berlin: Springer-Verlag).
10. Goeleven, D., Miettinen, M. and Panagiotopoulos, P.D., 1999, Dynamic hemivariational inequalities and their applications. Journal of Optimization Theory and Applications, 103(3), 567-601.
11. Goeleven, D., Motreanu, D., Dumont, Y. and Rochdi, M., 2003, Variational and Hemivariational Inequalities: Theory, Methods and Applications (Boston, Dordrecht, London: Kluwer Academic Publishers).
12. Han, W. and Sofonea, M., 2002, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity (International Press, American Mathematical Society).
13. Lions, J.L., 1969, Quelques méthodes De Résolution Des Problémes Aux Limites Non Linéaires (Paris: Dunod).
14. Migórski, S., 1995, Existence and relaxation results for nonlinear second order evolution inclusions. Discussiones Mathematicae. Differential Inclusions, 15, 129-148.
15. Migórski, S., 1995, Existence, variational and optimal control problems for nonlinear second order evolution inclusions. Dynamic Systems and Applications, 4, 513-528.
16. Migórski, S., 2000, Existence and convergence results for evolution hemivariational inequalities. Topological Methods in Nonlinear Analysis, 16, 125-144.
17. Migórski, S., 2005, Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction. Applicable Analysis, 84(7), 669-699.
18. Migórski, S. and Ochal, A., 2004, Boundary hemivariational inequality of parabolic type. Nonlinear Analysis. Theory, Methods Nonlinear Analysis. Theory, Methods & Applications, 57(4), 579-596.
19. Migórski, S. and Ochal, A., 2005, A unified approach to dynamic contact problems in viscoelasticity. Journal of Elasticity (In press).
20. Mistakidis, E.S. and Panagiotopoulos, P.D., 1998, The search for substationarity points in the unilateral contact problems with nonmonotone friction. Mathematical and Computer Modelling, 28(4-8), 341-358.
21. Naniewicz, Z. and Panagiotopoulos, P.D., 1995. Mathematical Theory of Hemivariational Inequalities and Applications (New York-Basel-Hong Kong: Marcel Dekker, Inc.).
22. Ochal, A., 2005, Existence results for evolution hemivariational inequalities of second order. Nonlinear Analysis. Theory, Methods & Applications, 60, 1369-1391.
23. Panagiotopoulos, P.D., 1985, Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions (Basel: Birkhäuser).
24. Panagiotopoulos, P.D., 1993, Hemivariational Inequalities, Applications in Mechanics and Engineering. (Berlin: Springer-Verlag).
25. Panagiotopoulos, P.D., 1995, Modelling of nonconvex nonsmooth energy problems: dynamic hemivariational inequalities with impact effects. Journal of Computational and Applied Mathematics, 63, 123-138.
26. Papageorgiou, N.S., 1992, Optimal control of nonlinear second order evolution equations. Glasnik Matematicki, 27, 297-311.
27. Tolstonogov, A.A., 2002, Properties of the set of extreme solutions for a class of nonlinear second order evolution inclusions, Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications, 10, 53-77.
28. Zeidler, E., 1990, Nonlinear Functional Analysis and Applications II A/B (New York: Springer).