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On nonlinear, nonconvex evolution inclusions

Nikolaos S. Papageorgiou — 1995

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, G δ -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.

Topological properties of the solution set of a class of nonlinear evolutions inclusions

Nikolaos S. Papageorgiou — 1997

Czechoslovak Mathematical Journal

In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F ( t , x ) , we are able to show that the solution set is in fact an R δ -set. Finally some applications to infinite dimensional control systems are also presented.

Boundary value problems and periodic solutions for semilinear evolution inclusions

Nikolaos S. Papageorgiou — 1994

Commentationes Mathematicae Universitatis Carolinae

We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.

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.

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