Abstract: We consider the fractional stochastic heat type equation with nonnegative bounded initial condition, and with noise term that behaves in space like the Riesz kernel and is possibly correlated in time, in the unit open ball centered at the origin in \(\mathbb{R}^d\). When the noise term is white in time, we establish a change in the growth of the solution of these equations depending on the noise level. On the other hand when the noise term behaves in time like the fractional Brownian motion with index \(H\in(1/2,1)\), we also derive explicit bounds leading to a well-known intermittency property.
These results are our recent joint work with Mohammud Foondun and Ngartelbaye (Serge) Guerngar.