Scalar conservation laws with monotone pure-jump Markov initial conditions

• 成果类型: Article
• 署名作者: Kaspar, David C.; Rezakhanlou, Fraydoun
• 署名单位: Brown University; University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0648-2
• 发表日期: 2016
• 页码: 867-899
• 关键词: burgers-equation; sticky particles; statistics; shocks

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.