Stochastic heat equation with rough dependence in space

This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H.(14,12) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient .(u) is differentiable with a Lipschitz derivative and .(0)=0.