Finite speed of propagation for stochastic porous media equations

TL;DR

This paper establishes finite speed of propagation for stochastic porous media equations driven by rough signals, providing explicit estimates and analyzing the fractal dimension of the associated random attractor.

Contribution

It introduces a novel proof of finite speed of propagation for stochastic porous media equations with rough signals, including fractional Brownian motion, and links this to the attractor's fractal dimension.

Findings

Finite speed of propagation is proven for equations driven by rough signals.

Explicit estimates for the propagation speed are provided.

The random attractor has infinite fractal dimension.

Abstract

We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving signal, thus including fractional Brownian motion for all Hurst parameters. The explicit estimates are then used to prove that the corresponding random attractor has infinite fractal dimension.