Fractional stochastic heat equation with piecewise constant coefficients

Abstract

We introduce a fractional stochastic heat equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.Here the coefficients A and ρ have the following form A(x) = a 1 1 {x≤0} + a 2 1 {x>0} and ρ(x) = ρ 1 1 {x≤0} + ρ 2 1 {x>0} , 2010 Mathematics Subject Classification. 60G22, 60H15, 35R60.

On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

“…where C is a constant depending only on the coefficient β, a 1 and a 2 . On the other hand, by Corollary 2.1 fromMishura et al (2019), we have that…”