Fractional stochastic heat equation with piecewise constant coefficients

TL;DR

This paper studies a fractional stochastic heat equation with piecewise constant coefficients driven by fractional Brownian motion, establishing fundamental solutions and proving existence and uniqueness of solutions.

Contribution

It introduces a new fractional stochastic heat equation with piecewise constant coefficients and characterizes its fundamental solution, proving well-posedness.

Findings

Fundamental solution characterized for the deterministic part.

Existence and uniqueness of the stochastic solution proven.

Analysis extends to equations driven by fractional Brownian motion.

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.