Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

Abstract EN

We consider the stochastic heat equation of the form ∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H, where W˙H is the fractional noise, L˙ is a (pure jump) Lévy space-time white noise, Δ is Laplacian, and Δα=-(-Δ)α/2 is the fractional Laplacian generator on R, and f,σ:[0,T]×R×R→R are measurable functions.

We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.