Some properties of non-linear fractional stochastic heat equations on bounded domains

16 Dec 2016 · Foondun Mohammud, Guerngar Ngartelbaye, Nane Erkan ·

Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ \xi\sigma (u_t(x)) \dot F(t,x), \end{equation*} where $\xi$ is a positive parameter and $\sigma$ is a globally Lipschitz continuous function. The stochastic forcing term $\dot F(t,x)$ is white in time but possibly colored in space. The operator $\mathcal{L}$ is a non-local operator. We study the behaviour of the solution with respect to the parameter $\xi$, extending the results in \cite{FoonNual} and \cite{Bin}

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Some properties of non-linear fractional stochastic heat equations on bounded domains

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