On stochastic porous-medium equations with critical-growth conservative multiplicative noise
On stochastic porous-medium equations with critical-growth conservative multiplicative noise
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DOI：
10.3934/dcds.2020388
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发表时间：
2021-06
影响因子：
1.1
通讯作者：
N. Dirr;Hubertus Grillmeier;Guenther Grün
中科院分区：
文献类型：
--
作者：
N. Dirr;Hubertus Grillmeier;Guenther Grün
首先，我们证明了在Ito意义下，受保守的乘性幂函数噪声驱动的随机多孔介质方程的鞅解的存在性、非负性和轨道唯一性。我们依赖于基于空间有限元离散、齐性论证和随机紧致性的能量方法。其次，我们使用蒙特卡罗模拟研究了噪声对等待时间和自由边界传播的影响。我们发现强有力的证据表明，平均而言，噪声会显著加速传播并减少等待时间的大小--特别是改变等待时间大小的标度律。
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.