ON STOCHASTIC POROUS-MEDIUM EQUATIONS WITH CRITICAL-GROWTH CONSERVATIVE MULTIPLICATIVE NOISE

Dirr N, Grillmeier H, Grün G (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Discrete and Continuous Dynamical Systems American Institute of Mathematical Sciences (AIMS)

Book Volume: 41

Pages Range: 2829-2871

Journal Issue: 6

DOI: 10.3934/dcds.2020388

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.

Authors with CRIS profile

Hubertus Grillmeier Professur für Angewandte Mathematik (Analysis und Numerik partieller Differentialgleichungen) Günther Grün Professur für Angewandte Mathematik (Analysis und Numerik partieller Differentialgleichungen)

Involved external institutions

Cardiff University GB United Kingdom (GB)

How to cite

APA:

Dirr, N., Grillmeier, H., & Grün, G. (2021). ON STOCHASTIC POROUS-MEDIUM EQUATIONS WITH CRITICAL-GROWTH CONSERVATIVE MULTIPLICATIVE NOISE. Discrete and Continuous Dynamical Systems, 41(6), 2829-2871. https://dx.doi.org/10.3934/dcds.2020388

MLA:

Dirr, Nicolas, Hubertus Grillmeier, and Günther Grün. "ON STOCHASTIC POROUS-MEDIUM EQUATIONS WITH CRITICAL-GROWTH CONSERVATIVE MULTIPLICATIVE NOISE." Discrete and Continuous Dynamical Systems 41.6 (2021): 2829-2871.

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