A SINGULAR LIMIT PROBLEM FOR THE IBRAGIMOV-SHABAT EQUATION

被引：1

作者：

Coclite, Giuseppe Maria ^{[1
]}

di Ruvo, Lorenzo ^{[2
]}

机构：

[1] Univ Bari, Dept Math, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Modena & Reggio Emilia, Dept Sci & Methods Engn, Via G Amendola 2, I-42122 Reggio Emilia, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2016年 / 9卷 / 03期

关键词：

Singular limit; compensated compactness; Ibragimov-Shabat equation; entropy condition; NONLINEAR EVOLUTION-EQUATIONS; CONSERVATION-LAWS; BACKLUND-TRANSFORMATIONS; CONVERGENCE;

D O I：

10.3934/dcdss.2016020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Ibragimov-Shabat equation, which contains non-linear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak 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.

引用

页码：661 / 673

页数：13

共 27 条

[1]

ABLOWITZ MJ, 1974, STUD APPL MATH, V53, P249

[2]

[Anonymous], APPL ANAL

[3]

BEALS R, 1989, STUD APPL MATH, V81, P125

[4]

Coclite G. M., ANN MAT PUR IN PRESS