ON THE NUMERICAL INTEGRATION OF SCALAR NONLOCAL CONSERVATION LAWS

被引：62

作者：

Amorim, Paulo ^{[1
]}

Colombo, Rinaldo M. ^{[2
]}

Teixeira, Andreia ^{[3
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil

[2] Univ Brescia, Unita INdAM, I-25123 Brescia, Italy

[3] Univ Lisbon, Dept Matemat, Ctr Matemat & Aplicacoes Fundamentais, P-1649003 Lisbon, Portugal

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2015年 / 49卷 / 01期

关键词：

Nonlocal conservation laws; Lax Friedrichs scheme; BALANCE LAWS; SEDIMENTATION; COEFFICIENTS; POPULATIONS; WAVES; FLOW;

D O I：

10.1051/m2an/2014023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a rather general class of 1D nonlocal conservation laws from a numerical point of view. First, following [F. Betancourt, R. Burger, K. H. Karlsen and E. M. Tory, On nonlocal conservation laws modelling sedimentation. Nonlinearity 24 ( 2011) 855-885], we define an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various analytical properties, obtaining evidence that usual properties of standard conservation laws fail in the nonlocal setting. Moreover, on the basis of our numerical integrations, we are led to conjecture the convergence of the nonlocal equation to the local ones, although no analytical results are, to our knowledge, available in this context.

引用

页码：19 / 37

页数：19

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