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Russian Mathematical Surveys, 2008, Volume 63, Issue 2, Pages 283–350
DOI: https://doi.org/10.1070/RM2008v063n02ABEH004516 (Mi rm9182) 		 
This article is cited in 36 scientific papers (total in 37 papers)

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

A. G. Kulikovskii, A. P. Chugainova

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (2341 kB) Citations (37)
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DOI: https://doi.org/10.1070/RM2008v063n02ABEH004516
Abstract: 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.
Received: 05.02.2008
Russian version:
Uspekhi Matematicheskikh Nauk, 2008, Volume 63, Issue 2(380), Pages 85–152
DOI: https://doi.org/10.4213/rm9182
Bibliographic databases:
Document Type: Article
UDC: 531.01
MSC: Primary 74H25; Secondary 35L65, 35L67, 35Q72, 74E10, 74H45, 74B20, 74J30
Language: English
Original paper language: Russian
Citation: A. G. Kulikovskii, A. P. Chugainova, “Classical and non-classical discontinuities in solutions of equations of non-linear elasticity theory”, Uspekhi Mat. Nauk, 63:2(380) (2008), 85–152; Russian Math. Surveys, 63:2 (2008), 283–350
Citation in format AMSBIB
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    • This publication is cited in the following 37 articles:
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