OSCILLATORY WAVES IN DISCRETE SCALAR CONSERVATION LAWS

被引：6
|
作者：
Herrmann, Michael [1 ]
机构：
[1] Univ Saarland, Dept Math, D-66123 Saarbrucken, Germany
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2012年 / 22卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
Conservation laws; difference schemes; dispersive shocks; traveling waves; Hamiltonian lattices; variational integrators; SMALL DISPERSION LIMIT; TRAVELING-WAVES; SOLITARY WAVES;
D O I：
10.1142/S021820251200585X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of a three-parameter family of periodic traveling waves (wavetrains). The proof is based on an integral equation for the dual wave profile and employs constrained maximization as well as the invariance properties of a gradient flow. We also discuss the approximation of wavetrains and present some numerical results.
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页数：21
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