On some properties of a class of fractional stochastic heat equations
journal contributionposted on 16.06.2016 by Wei Liu, Kuanhou Tian, Mohammud Foondun
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We consider nonlinear parabolic stochastic equations of the form ∂tu = Lu + λσ(u) ˙ξ on the ball B(0, R), where ˙ξ denotes some Gaussian noise and σ is Lipschitz continuous. Here L corresponds to a symmetric α-stable process killed upon exiting B(0, R). We will consider two types of noises: space-time white noise and spatially correlated noise. Under a linear growth condition on σ, we study growth properties of the second moment of the solutions. Our results are significant extensions of those in Foondun and Joseph (Stoch Process Appl, 2014) and complement those of Khoshnevisan and Kim (Proc AMS, 2013, Ann Probab, 2014).
Research supported in part by EPSRC.
- Mathematical Sciences