The initial-boundary value problem for general non-local scalar conservation laws in one space dimension

被引：21
作者：
De Filippis, Cristiana [1 ,2 ]
Goatin, Paola [1 ]
机构：
[1] Inria Sophia Antipolis Mediterranee, Biot, France
[2] Univ Oxford, Math Inst, Oxford, England
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 161卷
关键词：
Scalar conservation laws; Non-local flux; Initial-boundary value problem; Lax-Friedrichs scheme; LOOK-AHEAD DYNAMICS; TRAFFIC FLOW; WELL-POSEDNESS; MODEL; SIMULATION; EQUATION; VELOCITY; SCHEMES; SYSTEMS;
D O I：
10.1016/j.na.2017.05.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a global well-posedness result for a class of weak entropy solutions of bounded variation (BV) of scalar conservation laws with non-local flux on bounded domains, under suitable regularity assumptions on the flux function. In particular, existence is obtained by proving the convergence of an adapted Lax-Friedrichs algorithm. Lipschitz continuous dependence from initial and boundary data is derived applying KruZhkov's doubling of variable technique. (C) 2017 Elsevier Ltd. All rights reserved.
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页码：131 / 156
页数：26
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