This article is cited in 4 scientific papers (total in 4 papers)
Special discontinuities in nonlinearly elastic media
A. P. Chugainova
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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.
special discontinuities, generalized KdV-Burgers equation, self-similar Riemann problem, nonuniqueness of solutions.
|Russian Science Foundation
|This work was supported by the Russian Science Foundation under grant 14-50-00005.
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Computational Mathematics and Mathematical Physics, 2017, 57:6, 1013–1021
A. P. Chugainova, “Special discontinuities in nonlinearly elastic media”, Zh. Vychisl. Mat. Mat. Fiz., 57:6 (2017), 1023–1032; Comput. Math. Math. Phys., 57:6 (2017), 1013–1021
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\paper Special discontinuities in nonlinearly elastic media
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
A. G. Kulikovskii, A. P. Chugainova, “Long nonlinear waves in anisotropic cylinders”, Comput. Math. Math. Phys., 57:7 (2017), 1194–1200
A. G. Kulikovskii, A. P. Chugainova, “Shock waves in anisotropic cylinders”, Proc. Steklov Inst. Math., 300 (2018), 100–113
A. G. Kulikovskii, E. I. Sveshnikova, “Problem of the motion of an elastic medium formed at the solidification front”, Proc. Steklov Inst. Math., 300 (2018), 86–99
V. A. Shargatov, A. P. Chugainova, S. V. Gorkunov, S. I. Sumskoi, “Flow structure behind a shock wave in a channel with periodically arranged obstacles”, Proc. Steklov Inst. Math., 300 (2018), 206–218
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