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A class of semilinear stochastic partial differential equations and their controls: Existence results

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  • Zhou, Xun Yu

Abstract

This paper concerns a class of similinear stochastic partial differential equations, of which the drift term is a second-order differential operator plus a nonlinearity, and the diffusion term is a first-order differential operator. When the nonlinearity is only continuous in the state, it is shown that there exist solutions of the equation provided that the Wiener process involved is one-dimensional. The existence of optimal relaxed controls for this class of equations is also proved. Our method is based on a group analysis of the first-order differential operator and a time change technique.

Suggested Citation

  • Zhou, Xun Yu, 1993. "A class of semilinear stochastic partial differential equations and their controls: Existence results," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 89-106, January.
    • Handle: RePEc:eee:spapps:v:44:y:1993:i:1:p:89-106
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