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) + F(x(t)), without any Lipschitz conditions on the multi-function F.
@article{bwmeta1.element.doi-10_2478_s11533-011-0051-x,
author = {Alina Lazu and Victor Postolache},
title = {Approximate weak invariance for semilinear differential inclusions in Banach spaces},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1143-1155},
zbl = {1247.34110},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0051-x}
}
Alina Lazu; Victor Postolache. Approximate weak invariance for semilinear differential inclusions in Banach spaces. Open Mathematics, Tome 9 (2011) pp. 1143-1155. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0051-x/
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