Moment bounds for some fractional stochastic heat equations on the ball

TL;DR

This paper derives bounds for the moments of solutions to fractional stochastic heat equations on a ball, considering Gaussian noise with Riesz kernel spatial correlation and the white noise case on an interval.

Contribution

It provides new upper and lower moment bounds for fractional stochastic heat equations with specific noise types, extending understanding of their solution behavior.

Findings

Established moment bounds for fractional stochastic heat equations.

Analyzed equations driven by Riesz kernel correlated noise.

Extended results to space-time white noise case on an interval.

Abstract

In this paper, we obtain upper and lower bounds for the moments of the solution to a class of fractional stochastic heat equations on the ball driven by a Gaussian noise which is white in time, and with a spatial correlation in space of Riesz kernel type. We also consider the space-time white noise case on an interval.