Weakly nonlinear surface waves and subsonic phase boundaries

被引:8
作者
Benzoni-Gavage, S. [1 ,2 ]
Rosini, M. D. [3 ,4 ]
机构
[1] Univ Lyon 1, INSA Lyon, F-69621 Villeurbanne, France
[2] Ecole Cent Lyon, CNRS, Inst Camille Jordan, UMR5208, F-69622 Villeurbanne, France
[3] Univ Brescia, Dept Math, I-25133 Brescia, Italy
[4] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
关键词
Amplitude equation; Nonlocal Burgers equation; Subsonic phase transitions; STABILITY;
D O I
10.1016/j.camwa.2008.12.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The aim of this work is twofold. In a first, abstract part, it is shown how to derive an asymptotic equation for the amplitude of weakly nonlinear surface waves associated with neutrally stable undercompressive shocks. The amplitude equation obtained is a non-local generalization of Burgers' equation, for which an explicit stability condition is exhibited. This is an extension of earlier results by J. Hunter. The second part is devoted to 'ideal' subsonic phase boundaries, which were shown by the first author to be associated with linear surface waves. The amplitude equation for corresponding weakly non-linear surface waves is calculated explicitly and the stability condition is investigated analytically and numerically. (C) 2009 Elsevier Ltd. All rights reserved.
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页码:1463 / 1484
页数:22
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