On the convergence of the modified Rosenau and the modified Benjamin-Bona-Mahony equations

被引：11

作者：

Coclite, Giuseppe Maria ^{[1
]}

di Ruvo, Lorenzo ^{[2
]}

机构：

[1] Univ Bari, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Modena & Reggio Emilia, Dipartimento Sci & Metodi Ingn, Via G Amendola 2, I-42122 Reggio Emilia, Italy

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 74卷 / 05期

关键词：

Singular limit; Compensated compactness; Modified Rosenau equation; Modified Benjamin-Bona-Mahony equation; Entropy condition; SOLITARY WAVE SOLUTIONS; SINGULAR LIMIT PROBLEM; CONSERVATION-LAWS; KDV; COLLOCATION; ENTROPY; SCHEME; MODEL;

D O I：

10.1016/j.camwa.2016.02.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the modified Rosenau and the modified Benjamin-Bona-Mahony equations, which contain nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equations converge to entropy solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L-p setting.(C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：899 / 919

页数：21

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