On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise

Abstract

In this paper, we study a class of nonlinear stochastic heat equations ∂∂tu(t,x)=Δ+aαΔα2+b⋅∇u(t,x)+σ(u(t,x))Ẇ(t,x), where Ẇ denotes the Gaussian noise which is white in time and spatially homogeneous in space. The existence, uniqueness and the Hölder continuity of the mild solution to the above equation are proved.