Speaker: Dr. Erkan Nane

Title: Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains

Abstract: In this talk we study non-linear noise excitation for a class of space-time fractional stochastic equations in  bounded domains with Dirichlet  boundary conditions. These equations  were recently  introduced by Mijena and Nane, "Space time fractional stochastic partial differential equations" (Stochastic Process Appl. 125 (2015), no. 9, 3301--3326).   We first study  the existence and uniqueness of the solution of these equations  under suitable conditions on the initial function. We also study the asymptotic behavior of the solution  with respect to a parameter $\lambda$- intermittency. In particular, our results are significant extensions of those  in  M. Foondun, K. Tian and  W. Liu, "On some properties  of a class of fractional stochastic equations" (Preprint available at arxiv.org 1404.6791v1). We will also discuss some open problems on these space-time fractional equations.