Long-Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws
Long-Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws
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DOI：
10.1002/cpa.21646
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发表时间：
2017-08-01
影响因子：
3
通讯作者：
Souganidis, Panagiotis E.
中科院分区：
文献类型：
--
作者：
Gess, Benjamin;Souganidis, Panagiotis E.
研究了具有时间随机空间齐次流和周期初值的随机标量守恒律方程的路径熵解的长时间行为和正则性。我们证明了解收敛于其空间平均值，这是相关随机动力系统的唯一不变测度，并提供了收敛速率，即使在维度大于2的确定性情况下，后者也是新的。主要的工具是一个新的正则化结果的精神平均引理的标量守恒律，特别是，这意味着一个正则化的路径拟解的噪声型结果。(c)2016 Wiley Periodicals，Inc.
We study the long-time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random-in-time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure of the associated random dynamical system, and provide a rate of convergence, the latter being new even in the deterministic case for dimensions higher than 2. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise-type result for pathwise quasi-solutions.(c) 2016 Wiley Periodicals, Inc.