Finite speed of propagation for stochastic porous media equations

2012/10/08 by Benjamin Gess, Gess, Benjamin · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · #37L30 (Secondary) #37L55 #60H15 (Primary) 76S05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1210.2415

openalex publication_date 2012/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases

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