On average controllability of random heat equations with arbitrarily distributed diffusivity. (English) Zbl 1415.93044
Summary: In this paper, we study the average controllability of a random heat equation, with the diffusivity serving as the random variable drawn from a general probability distribution. We show that the solutions of such random heat equations are both null and approximately controllable in average from an arbitrary open set of the domain and in an arbitrarily small time, recovering the known result when the random diffusivity is uniformly or exponentially distributed.
MSC:
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35Q93 | PDEs in connection with control and optimization |
| 35K05 | Heat equation |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
Keywords:
partial differential equations; controllability; ensemble control systems; random heat equationReferences:
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