Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions

• 来源期刊: 偏微分方程(英文版)
• 学科: 数学
• 关键词: System of discrete Boltzmann equations BV solutions existence and uniqueness
• 年，卷（期）: 2009,（2）
• 页码范围: 127-152
• 页数: 26页
• 分类号: O175.2
• 语种: 英文

摘要

The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions (2000). The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form etf∫i+(∫mii)x=Qi(∫1,∫2,…,∫n), (mi1, i=1,…,n) with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.