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Optimal control of nonlinear evolution equations

Nikolaos S. PapageorgiouNikolaos Yannakakis — 2001

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls. Then we pass to nonparametric...

Existence of extremal periodic solutions for nonlinear evolution inclusions

Nikolaos S. PapageorgiouNikolaos Yannakakis — 2001

Archivum Mathematicum

We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.

Multiple solutions for nonlinear periodic problems with discontinuities

Nikolaos S. PapageorgiouNikolaos Yannakakis — 2002

Archivum Mathematicum

In this paper we consider a periodic problem driven by the one dimensional p -Laplacian and with a discontinuous right hand side. We pass to a multivalued problem, by filling in the gaps at the discontinuity points. Then for the multivalued problem, using the nonsmooth critical point theory, we establish the existence of at least three distinct periodic solutions.

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