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1995 | 15 | 1 | 29-42
Tytuł artykułu

On nonlinear, nonconvex evolution inclusions

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, $G_δ$-subset of the solution set of the original Cauchy problem. As an application, we obtain "bang-bang"' type theorems for two nonlinear parabolic distributed parameter control systems.
Twórcy
  • Florida Institute of Technology, Department of Applied Mathematics, 150 West University Blvd. Melbourne, Florida 32901-6988, USA
Bibliografia
  • [1] E. Avgerinos, N. S. Papageorgiou, Nonconvex perturbations of evolution equations with m-dissipative operators in Banach spaces, Comment. Math. Univ. Carol. 30 (1989), 657-664.
  • [2] E. Balder, Necessary and sufficient conditions for L₁-strong-weak lower semicontinuity of integral functionals, Nonlin. Anal.-TMA 11 (1987), 1399-1404.
  • [3] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Intern. Publishing, Leyden, The Netherlands 1976.
  • [4] M. Benamara, Points Extrémaux, Multi-applications et Fonctionelles Intégrales, These du 3eme Cycle, Université de Grenoble, France 1975.
  • [5] Ph. Benilan, Equations d'Evolution dans un Espace de Banach Quelconque et Applications, These, Université de Paris XI, Orsay 1972.
  • [6] H. Brezis, Operateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North Holland, Amsterdam 1973.
  • [7] H. Brezis, Problemes unilateraux, J. Math. Pures et Appl. 51 (1972), 1-164.
  • [8] F. S. DeBlasi, G. Pianigiani, Nonconvex valued differential inclusions in Banach spaces, J. Math. Anal. Appl. 157 (1991), 469-494.
  • [9] A. Fryszkowski, Continuous selections for a class of nonconvex multivalued maps, Studia Math. 78 (1983), 163-174.
  • [10] S. Gutman, Topological equivalence in the space of integrable vector-valued functions, Proc. Amer. Math. Soc. 93 (1985), 40-42.
  • [11] S. Gutman, Evolutions governed by m-accretive plus compact operators, Nonl. Anal.-TMA 7 (1983), 707-715.
  • [12] V. Lakshmikantham, S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, London 1981.
  • [13] E. Mitidieri, I. Vrabie, Differential inclusions governed by nonconvex perturbations of m-accretive operators, Differ. and Int. Equations 2 (1989), 525-531.
  • [14] G. Pianigiani, Differential inclusions: The Baire category method, Proc. CIME, Varenna, ed. by A. Cellina, Lecture Notes in Math. No. 1446, Springer-Verlag, Berlin 1990.
  • [15] A. Tolstonogov, Extreme continuous selectors of multivalued maps and their applications, Preprint SISSA 72M (June, 1991), Trieste, Italy. (Also Soviet Math. Doklady 43 (2) (1991), 481-485).
  • [16] D. Wagner, Survey of measurable selection theorems, SIAM J. Control. Optim. 15 (1977), 859-903.
  • [17] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-div15i1n4bwm
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