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Abstract

Abstract Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.
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Abstract

Abstract Various optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.
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Abstract

Praca zawiera analizy i oceny skutków wybranych regulacji polskiego prawa dotyczących gospodarki przestrzennej, zwłaszcza planowania przestrzennego. Różni się od poprzednich raportów położeniem większego nacisku na bariery blokujące naprawę wadliwego systemu publicznego zarządzania przestrzenią. Praca nie jest próbą oceny prawa pod względem jego poprawności jurydycznej i legislacyjnej.
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