PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 15 | 2 | 129-148
Tytuł artykułu

Existence and relaxation results for nonlinear second order evolution inclusions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.
Twórcy
  • Institute for Information Sciences, Jagellonian University, Nawojki 11, 30-072 Cracow, Poland
Bibliografia
  • [1] N.U. Ahmed, Existence of optimal controls for a class of systems governed by differential inclusions in Banach spaces, J. Optimization Theory and Appl. 50 (2) (1986), 213-237.
  • [2] N.U. Ahmed, Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc., N. H. Pavel, Editor, New York, Basel, Hong Kong 160 (1994), 1-19.
  • [3] N.U. Ahmed and S. Kerbal, Optimal control of nonlinear second order evolution equations, J. Applied Math. and Stochastic Anal. 6 (1993), 123-136.
  • [4] N.U. Ahmed and K.L.Teo, Optimal Control of Distributed Parameter Systems, North Holland, New York 1981.
  • [5] J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-Heidelberg, New York, Tokyo 1984.
  • [6] V.Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leyden, The Netherlands 1976.
  • [7] H. Brezis, Opérateurs maximaux monotones et semi-groups de contractions dans les espaces de Hilbert, North-Holland, Amsterdam 1973.
  • [8] H.O. Fattorini, Existence theory and the maximum principle for relaxed infinite-dimensional optimal control problems, SIAM J. Control and Optimization 32 (2) (1994), 311-331.
  • [9] A.F. Filipov, Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621.
  • [10] A. Fryszkowski, Continuous selections for nonconvex multivalued maps, Studia Math. 76 (1983), 163-174.
  • [11] S. Hu, V. Lakshmikantham and N.S. Papageorgiou, On the solution set of nonlinear evolution inclusions, Dynamics Systems and Appl. 1 (1992), 71-82.
  • [12] K. Kuratowski, Topology, Academic Press N.Y. and PWN-Polish Scientific Publishers, Vol. I, Warszawa 1966.
  • [13] J.L. Lions, Quelques méthodes de résolution des problémes aux limites non linéaires, Dunod, Paris 1969.
  • [14] J.L. Lions and E. Magenes, Problémes aux limites non homogénes et applications, Dunod, Paris 1 (1968).
  • [15] S. Migórski, A counterexample to a compact embedding theorem for functions with values in a Hilbert space, Proc. Amer. Math. Soc. 123 (8) (1995), 2447-2449.
  • [16] S. Migórski, Existence and relaxation results for nonlinear evolution inclusions revisited, J. Applied Math. and Stochastic Anal. 8 (2) (1995), 143-149.
  • [17] E.V. Nagy, A theorem on compact embedding for functions with values in an infinite dimensional Hilbert space, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 22-23 (1979-80), 243-245.
  • [18] N.S. Papageorgiou, Convergence theorems for Banach space valued integrable multifunctions, Intern. J. Math. and Math. Sci. 10 (1987), 433-442.
  • [19] N.S. Papageorgiou, A relaxation theorem for differential inclusions in Banach spaces, Tohoku Math. Journ. 39 (1987), 505-517.
  • [20] N.S. Papageorgiou, Measurable multifunctions and their applications to convex integral functionals, Internat. J. Math. and Math. Sci. 12 (1989), 175-192.
  • [21] N.S. Papageorgiou, Continuous dependence results for a class of evolution inclusions, Proc. of the Edinburgh Math. Soc. 35 (1992), 139-158.
  • [22] A. Pliś, Trajectories and quasitrajectories of an orientor field, Bull. Polish Acad. Sci. Math. 10 (1962), 529-531.
  • [23] J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl. (IV), Vol. CXLVI (1987), 65-96.
  • [24] A.A. Tolstonogov, Solutions of evolution inclusions, I, Sibirskii Matematicheskii Zhurnal 33 (1992), 161-174.
  • [25] D. Wagner, Survey of measurable selection theorems, SIAM J. Control Optim. 15 (1977), 859-903.
  • [26] T. Ważewski, Sur une généralisation de la notion des solutions d'une équation au contingent, Bull. Polish Acad. Sci. Math. 10 (1962), 11-15.
  • [27] J. Wloka, Partial differential equations, Cambridge University Press 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-div15i2n2bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.