Convergence of the Kuramoto-Sinelshchikov Equation to the Burgers One

被引：16
|
作者：
Coclite, Giuseppe Maria [1 ]
di Ruvo, Lorenzo [2 ]
机构：
[1] Univ Bari, Dept Math, Via 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：
ACTA APPLICANDAE MATHEMATICAE | 2016年 / 145卷 / 01期
关键词：
Singular limit; compensated compactness; Kuramoto; Sinelshchikov equation; entropy condition; SINGULAR LIMIT PROBLEM; SCALAR CONSERVATION-LAWS; NONLINEAR SATURATION; SIVASHINSKY EQUATION; WAVES; STABILITY; APPROXIMATIONS; STABILIZATION; INSTABILITY; ENTROPY;
D O I：
10.1007/s10440-016-0049-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Kuramoto-Sinelshchikov equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the setting.
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页码：89 / 113
页数：25
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