KINETIC SOLUTIONS FOR NONLOCAL SCALAR CONSERVATION LAWS

被引：7
|
作者：
Wei, Jinlong [1 ]
Duan, Jinqiao [2 ]
Lv, Guangying [3 ]
机构：
[1] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China
[2] IIT, Dept Appl Math, Chicago, IL 60616 USA
[3] Inst Appl Math, Kaifeng, Henan, Peoples R China
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 02期
基金：
中国博士后科学基金;
关键词：
kinetic solution; nonlocal conservation laws; uniqueness; existence; anomalous diffusion; BURGERS-EQUATION; FORMULATION; ADVECTION; SYSTEM;
D O I：
10.1137/16M108687X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work is devoted to examining the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal supercritical diffusion operator. Our proof for uniqueness is based upon the analysis of a microscopic contraction functional, and the existence is enabled by a parabolic approximation. As an illustration, we obtain the existence and uniqueness of kinetic solutions for the generalized fractional Burgers-Fisher-type equations. Moreover, we demonstrate the kinetic solutions' Lipschitz continuity in time and continuous dependence on nonlinearities and Levy measures.
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页码：1521 / 1543
页数：23
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