Scalar conservation laws with monotone pure-jump Markov initial conditions

被引：9
|
作者：
Kaspar, David C. [1 ]
Rezakhanlou, Fraydoun [2 ]
机构：
[1] Brown Univ, Div Appl Math, 182 George St,Box F, Providence, RI 02912 USA
[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2016年 / 165卷 / 3-4期
基金：
美国国家科学基金会;
关键词：
Scalar conservation laws; Random initial data; Markov jump processes; BURGERS-EQUATION; STICKY PARTICLES; STATISTICS; SHOCKS;
D O I：
10.1007/s00440-015-0648-2
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In 2010 Menon and Srinivasan published a conjecture for the statistical structure of solutions to scalar conservation laws with certain Markov initial conditions, proposing a kinetic equation that should suffice to describe as a stochastic process in x with t fixed. In this article we verify an analogue of the conjecture for initial conditions which are bounded, monotone, and piecewise constant. Our argument uses a particle system representation of over for , with a suitable random boundary condition at x = L.
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页码：867 / 899
页数：33
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