## Abstract

We solve a control problem for the stochastic Burgers equation using the dynamic programming approach. The cost functional involves exponentially growing functions and the analog of the kinetic energy; the case of a distributed parameter control is considered. The Hamilton-Jacobi equation is solved by a compactness method and a-priori estimates are obtained thanks to the regularizing properties of the transition semigroup associated to the stochastic Burgers equation; a fixed point argument does not seem to apply here.

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Entrata in Redazione il 10 dicembre 1998.

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Da Prato, G., Debussche, A. Dynamic programming for the stochastic burgers equation.
*Annali di Matematica pura ed applicata* **178, **143–174 (2000). https://doi.org/10.1007/BF02505893

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### Keywords

- Control Problem
- Dynamic Programming
- Mild Solution
- Burger Equation
- Galerkin Approximation