Some optimal control problems for partial differential inclusions

• Autorzy: Kisielewicz M.
• Języki publikacji: EN

Abstrakty

EN

Partial differential inclusions are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence theorems and some properties of solutions to partial differential inclusions are given.

Słowa kluczowe

EN

partial differential inclusions; diffusion processes; existence theorems

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 4
• Strony: 507--516
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kisielewicz M.

• University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics, ul. Podgórna 50, 65-246 Zielona Góra, Poland,

Bibliografia

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• [2] G. Bartuzel, A. Fryszkowski, Abstract differential inclusions Gwith some applications to partial differential ones, Ann. Polon. Math. LIII (1991), 67–78.
• [3] G. Bartuzel, A. Fryszkowski, Stability of Principal Eigenvalue of Schrodinger type problem for differential inclusions, Topol. Meth. Nonlinear Anal. 16 (2000), 181–194.
• [4] G. Bartuzel, A. Fryszkowski, A class of retracts in Lp with some applications to differential inclusions, Discuss. Math. Diff. Incl. Opt. 22 (2002), 213–224.
• [5] N. Ikeda, S. Watanabe, Stochastic Diferential Equations and Diffusion Processes, North Holand Publ., Amsterdam, 1981.
• [6] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ., New York, 1991.
• [7] M. Kisielewicz, Set-Valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 15 (1997) 5, 783–800.
• [8] M. Kisielewicz, Weak compactness of solution sets to stochastic differential inclusions with convex right hand sides, Topol. Math Nonlinear Anal. 18 (2001), 149–169.
• [9] M. Kisielewicz, Stochastic differential inclusions and diffusion processes, Journal Math. Anal. Appl. 334 (2007), 1039–1054.
• [10] M. Kisielewicz, Stochastic representation of partial differential inclusions, Journal Math. Anal. Appl. (presented to publish).
• [11] E. Michael, Continuous selections I, Ann. Math. 63 (1956), 361–382.
• [12] B. Øksendal, Stochastic Differential Equations, Springer Verlag, Berlin-Heildelberg, 1998.
• [13] D.W. Strook, S.R.S Varadhan, Diffusion process with continuous coeficients, I, II, Comm. Pure Appl. Math. 22 (1969), 345–400, 479–530.