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.

引用

页码：1521 / 1543

页数：23

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