In this paper, we consider variational optimal control problems. The state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator with a potential, with a right-hand side that may change sign. The control variable is the potential itself, that may vary in a suitable admissible class of non-negative potentials. The cost is an integral functional, linear (but non-monotone) with respect to the state function. We prove the existence of optimal potentials and we provide some necessary conditions for optimality. Several numerical simulations are shown.

Optimal potentials for problems with changing sign data

Giuseppe Buttazzo
;
Bozhidar Velichkov
2018

Abstract

In this paper, we consider variational optimal control problems. The state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator with a potential, with a right-hand side that may change sign. The control variable is the potential itself, that may vary in a suitable admissible class of non-negative potentials. The cost is an integral functional, linear (but non-monotone) with respect to the state function. We prove the existence of optimal potentials and we provide some necessary conditions for optimality. Several numerical simulations are shown.
Buttazzo, Giuseppe; Maestre, Faustino; Velichkov, Bozhidar
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/939293
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