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Article Dans Une Revue Journal of Optimization Theory and Applications Année : 2018

Optimal Potentials for Problems with Changing Sign Data

Résumé

In this paper, we consider variational optimal control problems. The state equation is an elliptic partial differential equation of a Schrödinger 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 nonnegative 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.
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Dates et versions

hal-02014035 , version 1 (11-02-2019)

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Giuseppe Buttazzo, Faustino Maestre, Bozhidar Velichkov. Optimal Potentials for Problems with Changing Sign Data. Journal of Optimization Theory and Applications, 2018, 178 (3), pp.743-762. ⟨10.1007/s10957-018-1347-9⟩. ⟨hal-02014035⟩
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