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Measure solutions for semilinear evolution equations with polynomial growth and their optimal control

N.U. Ahmed (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.

Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

N.U. Ahmed (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.

Méthodes du second ordre dans les problèmes d'optimisation avec contraintes

Auslender (1969)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Metric space valued functions of bounded variation

Luigi Ambrosio (1990)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Minimax control of nonlinear evolution equations

Nikolaos S. Papageorgiou (1995)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.