Average Controllability of Random Heat Equations
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In this thesis, we introduce random differential equations in an abstract framework and study their well-posedness. We study average controllability properties of a random heat equation when the diffusivity is a random variable. 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.