Approximate weak invariance for semilinear differential inclusions in Banach spaces

• Autorzy: Alina Lazu , Victor Postolache
• Języki publikacji: EN

Abstrakty

EN

In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + $\overline {co} $ F(x(t)), without any Lipschitz conditions on the multi-function F.

Słowa kluczowe

EN

Semilinear differential inclusion; Approximate weak invariance; ɛ-solution; Banach spaces; Relaxation

Kategorie tematyczne

• 47H04: Set-valued operators
• 34G25: Evolution inclusions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 1143-1155

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Alina Lazu

• “Al. I. Cuza” University

autor

Victor Postolache

• “Al. I. Cuza” University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0051-x