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.
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页码：899 / 919
页数：21
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