In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure mapping Σ × V to V* with Σ denoting the sigma algebra of subsets of the set I and f is a nonlinear operator mapping I × H to H, γ is a countably additive bounded positive measure and the control u is a suitable vector measure. We present existence, uniqueness and regularity properties of weak solutions and then prove the existence of optimal controls (vector valued measures) for a class of control problems.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1100,
author = {N.U. Ahmed},
title = {Optimal control of systems determined by strongly nonlinear operator valued measures},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {28},
year = {2008},
pages = {165-189},
zbl = {1191.35160},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1100}
}
N.U. Ahmed. Optimal control of systems determined by strongly nonlinear operator valued measures. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 28 (2008) pp. 165-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1100/
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