Stochastic non-isotropic degenerate parabolic–hyperbolic equations
Stochastic non-isotropic degenerate parabolic–hyperbolic equations
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DOI：
10.1016/j.spa.2017.01.005
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发表时间：
2016-11
影响因子：
1.4
通讯作者：
B. Gess;P. Souganidis
中科院分区：
文献类型：
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作者：
B. Gess;P. Souganidis
我们引入了一类具有非各向同性非线性和具有粗糙时间依赖性的通量的简并抛物双曲方程的路径熵解的概念，并证明了它们的适定性。在布朗噪声和周期性边界条件的情况下，我们证明了路径熵解收敛到其空间平均值，并提供了收敛速率的估计。论文的第三个主要结果是本着平均引理精神的新的正则化结果。这项工作将 Lions、Perthame 和 Souganidis 引入的随机标量守恒定律的路径熵解框架以及作者对随机标量守恒定律的长期行为的分析扩展到一类新的方程。
We introduce the notion of pathwise entropy solutions for a class of degenerate parabolic–hyperbolic equations with non-isotropic nonlinearity and fluxes with rough time dependence and prove their well-posedness. In the case of Brownian noise and periodic boundary conditions, we prove that the pathwise entropy solutions converge to their spatial average and provide an estimate on the rate of convergence. The third main result of the paper is a new regularization result in the spirit of averaging lemmata. This work extends both the framework of pathwise entropy solutions for stochastic scalar conservation laws introduced by Lions, Perthame and Souganidis and the analysis of the long time behavior of stochastic scalar conservation laws by the authors to a new class of equations.