A priori estimates for operational differential inclusions

Frankowska, Halina

Frankowska, Halina (1990), A priori estimates for operational differential inclusions, Journal of Differential Equations, 84, 1, p. 100-128. http://dx.doi.org/10.1016/0022-0396(90)90129-D

Type

Article accepté pour publication ou publié

Date

1990

Journal name

Journal of Differential Equations

Volume

Number

Publisher

Elsevier

Pages

100-128

Abstract (EN)

We prove a set-valued Gronwall lemma and a relaxation theorem for the semilinear differential inclusion x′ ϵAx + F(t, x), x(0) = x0, where A is the infinitesimal generator of a C0-semigroup on a separable Banach space X and F: [0, T] × X ↦ X is a set-valued map. This allows us to investigate infinitesimal generators of reachable sets and variational inclusions. The results are applied to a semilinear optimal control problem with end point constraints.

Subjects / Keywords

differential inclusions