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On stochastic porous-medium equations with critical-growth conservative multiplicative noise

Dirr, Nicolas, Grillmeier, Hubertus and Grün, Guenther 2021. On stochastic porous-medium equations with critical-growth conservative multiplicative noise. Discrete and Continuous Dynamical Systems - Series A 41 (6) , pp. 2829-2871. 10.3934/dcds.2020388
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First, we prove existence, nonnegativity, and pathwise uniqueness of martingale solutions to stochastic porous-medium equations driven by conservative multiplicative power-law noise in the Ito-sense. We rely on an energy approach based on finite-element discretization in space, homogeneity arguments and stochastic compactness. Secondly, we use Monte-Carlo simulations to investigate the impact noise has on waiting times and on free-boundary propagation. We find strong evidence that noise on average significantly accelerates propagation and reduces the size of waiting times – changing in particular scaling laws for the size of waiting times.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: American Institute of Mathematical Sciences (AIMS)
ISSN: 1078-0947
Funders: EPSRC
Date of First Compliant Deposit: 10 November 2020
Date of Acceptance: 31 August 2020
Last Modified: 11 Oct 2021 03:59

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