Near viability for fully nonlinear differential inclusions

• Autorzy: Irina Căpraru , Alina Lazu
• 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.

Słowa kluczowe

EN

Nonlinear differential inclusions; A priori estimates; Near viability

Kategorie tematyczne

• 47J35: Nonlinear evolution equations
• 34G20: Nonlinear equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 10
• Strony: 1447-1459

Daty

wydano

2014-10-01

online

2014-06-21

Twórcy

autor

Irina Căpraru

• “Al. I. Cuza” University of Iaşi

autor

Alina Lazu

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-014-0424-z