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2014 | 12 | 10 | 1447-1459
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Near viability for fully nonlinear differential inclusions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
10
Strony
1447-1459
Opis fizyczny
Daty
wydano
2014-10-01
online
2014-06-21
Twórcy
Bibliografia
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  • [10] Cârjă O., Necula M., Vrabie I. I., Necessary and sufficient conditions for viability for nonlinear evolution inclusions, Set-Valued Anal., 2008, 16(5–6), 701–731 http://dx.doi.org/10.1007/s11228-007-0063-7
  • [11] Cârjă O., Postolache V., Necessary and sufficient conditions for local invariance for semilinear differential inclusions, Set-Valued Var. Anal., 2011, 19(4), 537–554 http://dx.doi.org/10.1007/s11228-011-0173-0
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  • [17] Goreac D., Serea O.-S., Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems, Nonlinear Anal., 2010, 73(8), 2699–2713 http://dx.doi.org/10.1016/j.na.2010.06.050
  • [18] Lazu A. I., Postolache V., Approximate weak invariance for semilinear differential inclusions in Banach spaces, Cent. Eur. J. Math., 2011, 9(5), 1143–1155 http://dx.doi.org/10.2478/s11533-011-0051-x
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  • [20] Vrabie I. I., Compactness Methods for Nonlinear Evolutions, 2nd ed., Pitman Monogr. Surveys Pure Appl. Math., 75, Longman, New York, 1995
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0424-z
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