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

Foondun, Mohammud and Guerngar, Ngartelbaye and Nane, Erkan (2017) Some properties of non-linear fractional stochastic heat equations on bounded domains. Chaos, Solitons and Fractals. ISSN 0960-0779 (In Press)

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    Abstract

    Consider the following stochastic partial differential equation,∂tut(x) = Lut(x) + ξσ(ut(x)) ˙F (t, x),where ξ is a positive parameter and σ is a globally Lipschitz continuous function. The stochastic forcing term ˙F (t, x) is white in time but possibly colored in space. The operator L is a non-local operator. We study the behaviour of the solution with respect to the parameter ξ, extending the results in [8] and [11].