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Weak solutions of stochastic reaction diffusion equations and their optimal control

  • * Corresponding author: N.U.Ahmed

    * Corresponding author: N.U.Ahmed
The author is supported by NSERC grant A7109
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  • In this paper we consider a class of stochastic reaction diffusion equations with polynomial nonlinearities. We prove existence and uniqueness of weak solutions and their regularity properties. We introduce a suitable topology on the space of stochastic relaxed controls and prove continuous dependence of solutions on controls with respect to this topology and the norm topology on the natural space of solutions. Also we prove that the attainable set of measures induced by the weak solutions is weakly compact. Then we consider some optimal control problems, including the Bolza problem, and some target seeking problems in terms of the attainable sets in the space of measures and prove existence of optimal controls. In the concluding section we present briefly some extensions of the results presented here.

    Mathematics Subject Classification: Primary: 35R60, 49J20, 49J55, 93C20.

    Citation:

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