Evolution Equations and Control Theory (EECT)

Optimal control for stochastic heat equation with memory

Pages: 35 - 58, Volume 3, Issue 1, March 2014      doi:10.3934/eect.2014.3.35

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Fulvia Confortola - Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32 - 20133 Milano, Italy (email)
Elisa Mastrogiacomo - Dipartimento di statistica e metodi quantitativi, Universit√° degli studi di Milano Bicocca, Piazza dell'Ateneo Nuovo, 1 - 20126, Milano, Italy (email)

Abstract: In this paper, we investigate the existence and uniqueness of solutions for a class of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise.

Keywords:  Equations with memory, dynamical systems, semigroup theory, forward-backward systems, stochastic optimal control.
Mathematics Subject Classification:  Primary: 45D05, 93E20; Secondary: 60H30

Received: December 2012;      Revised: July 2013;      Available Online: February 2014.