# Approximate weak invariance for semilinear differential inclusions in Banach spaces

Open Mathematics (2011)

- Volume: 9, Issue: 5, page 1143-1155
- ISSN: 2391-5455

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topAlina Lazu, and Victor Postolache. "Approximate weak invariance for semilinear differential inclusions in Banach spaces." Open Mathematics 9.5 (2011): 1143-1155. <http://eudml.org/doc/269537>.

@article{AlinaLazu2011,

abstract = {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.},

author = {Alina Lazu, Victor Postolache},

journal = {Open Mathematics},

keywords = {Semilinear differential inclusion; Approximate weak invariance; ɛ-solution; Banach spaces; Relaxation; -solution},

language = {eng},

number = {5},

pages = {1143-1155},

title = {Approximate weak invariance for semilinear differential inclusions in Banach spaces},

url = {http://eudml.org/doc/269537},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Alina Lazu

AU - Victor Postolache

TI - Approximate weak invariance for semilinear differential inclusions in Banach spaces

JO - Open Mathematics

PY - 2011

VL - 9

IS - 5

SP - 1143

EP - 1155

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/269537

ER -

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