Classical and non-classical discontinuities in solutions of equations of non-linear elasticity theory

被引：30

作者：

Kulikovskii, A. G. ^{[1
]}

Chugainova, A. P. ^{[1
]}

机构：

[1] Russian Acad Sci, VA Steklov Math Inst, Moscow 117901, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2008年 / 63卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.1070/RM2008v063n02ABEH004516

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to a study of problems involving the propagation of one-dimensional non-linear waves of small amplitude in elastic media, using analytic and numerical methods. The equations of non-linear elasticity theory belong to the class of hyperbolic systems expressing conservation laws. For the unique construction of solutions it is necessary to supplement these equations with terms that make it possible to adequately describe actual small-scale phenomena, including the structure of the discontinuities that arise. The behaviour of non-linear waves is considered in two cases: when the small-scale processes are conditioned by viscosity, and when dispersion plays an essential role in addition to viscosity.

引用

页码：283 / 350

页数：68