Dirr N, Grillmeier H, Grün G (2021)
Publication Type: Journal article
Publication year: 2021
Book Volume: 41
Pages Range: 2829-2871
Journal Issue: 6
DOI: 10.3934/dcds.2020388
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.
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://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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