High order Anderson parabolic model driven by rough noise in space

Abstract

In this paper, we concern the fourth parabolic model on [Formula: see text] driven by a multiplicative Gaussian noise which behaves like fractional Brownian motion in time and space with Hurst index [Formula: see text] and [Formula: see text], respectively. The existence and uniqueness of mild solution in Skorohod sense are proved, and the weak intermittency is obtained by estimating [Formula: see text]th ([Formula: see text]) moment of the solution. Moreover, the Hölder continuity can be obtained for the time and space variable.