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

Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, 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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Abstract

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:	19 Nov 2024 00:30
URI:	https://orca.cardiff.ac.uk/id/eprint/136250

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