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  1. Computational Mathematics and Mathematical Physics
  2. Computational Mathematics and Mathematical Physics : Volume 57
  3. Computational Mathematics and Mathematical Physics : Volume 57, Issue 6, June 2017
  4. Special discontinuities in nonlinearly elastic media
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Computational Mathematics and Mathematical Physics : Volume 57
Computational Mathematics and Mathematical Physics : Volume 57, Issue 6, June 2017
Computation of zeros of the alpha exponential function
Synthesis of a rational filter in the presence of complete alternance
Parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points
A relation between two simple localized solutions of the wave equation
Parabolic equations with unknown time-dependent coefficients
On power series representing solutions of the one-dimensional time-independent Schrödinger equation
Well-posedness analysis and numerical implementation of a linearized two-dimensional bottom sediment transport problem
Stability of the Kolmogorov flow and its modifications
Special discontinuities in nonlinearly elastic media
Lebesgue averaging method in serial computations of atmospheric radiation
Application of numerical schemes with singling out the boundary layer for the computation of turbulent flows using eddy-resolving approaches on unstructured grids
Solution of the Wang Chang–Uhlenbeck equation for molecular hydrogen
Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink
Computational Mathematics and Mathematical Physics : Volume 57, Issue 5, May 2017
Computational Mathematics and Mathematical Physics : Volume 57, Issue 4, April 2017
Computational Mathematics and Mathematical Physics : Volume 57, Issue 3, March 2017
Computational Mathematics and Mathematical Physics : Volume 57, Issue 2, February 2017
Computational Mathematics and Mathematical Physics : Volume 57, Issue 1, January 2017
Computational Mathematics and Mathematical Physics : Volume 56
Computational Mathematics and Mathematical Physics : Volume 55
Computational Mathematics and Mathematical Physics : Volume 54
Computational Mathematics and Mathematical Physics : Volume 53
Computational Mathematics and Mathematical Physics : Volume 52
Computational Mathematics and Mathematical Physics : Volume 51
Computational Mathematics and Mathematical Physics : Volume 50
Computational Mathematics and Mathematical Physics : Volume 49
Computational Mathematics and Mathematical Physics : Volume 48
Computational Mathematics and Mathematical Physics : Volume 47
Computational Mathematics and Mathematical Physics : Volume 46

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Special discontinuities in nonlinearly elastic media

Content Provider Springer Nature Link
Author Chugaiva, A. P.
Copyright Year 2017
Abstract Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.
Starting Page 1013
Ending Page 1021
Page Count 9
File Format PDF
ISSN 09655425
Journal Computational Mathematics and Mathematical Physics
Volume Number 57
Issue Number 6
e-ISSN 15556662
Language English
Publisher Pleiades Publishing
Publisher Date 2017-07-01
Publisher Place Moscow
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword special discontinuities generalized KdV–Burgers equation self-similar Riemann problem nonuniqueness of solutions Computational Mathematics and Numerical Analysis
Content Type Text
Resource Type Article
Subject Computational Mathematics
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