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Start Over Subject evolution triple

1. On the existence of optimal controls for nonlinear infinite dimensional systems

Creator:
Fiacca, Antonella, Papageorgiou, Nikolaos S., and Papalini, Francesca
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
evolution triple, optimal control, monotone operation, hemicontinuous operator, parabolic system, and property $(Q)$
Language:
English
Description:
We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Periodic problems and problems with discontinuities for nonlinear parabolic equations

Creator:
Cardinali, Tiziana and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
pseudomonotone operator, $L$-pseudomonotonicity, operator of type $(S)_{+}$, operator of type $L$-$(S)_{+}$, coercive operator, surjective operator, evolution triple, compact embedding, multifunction, upper solution, lower solution, extremal solution, and $R_{\delta }$-set
Language:
English
Description:
In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact $R_{\delta }$-set in $(CT,L^2(Z))$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public