Approximate weak invariance for semilinear differential inclusions in Banach spaces

Alina Lazu; Victor Postolache

Open Mathematics (2011)

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

Abstract

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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) + c o ¯ F(x(t)), without any Lipschitz conditions on the multi-function F.

How to cite

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Alina 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 -

References

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