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.
Entropy solutions for stochastic porous media equations
Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
Propagation of chaos: a review of models, methods and applications. I. Models and methods
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