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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 1034–1055 (Mi zvmmf4578)  

This article is cited in 14 scientific papers (total in 16 papers)

Symmetric hyperbolic equations in the nonlinear elasticity theory

S. K. Godunov, I. M. Peshkov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: The basic results are overviewed concerning the formulation of nonlinear elasticity equations in the form of symmetric hyperbolic systems in long-time studies performed under the direction of the first author. The underlying principles developed in those studies are stated, and some inaccuracies and errors are corrected. Procedures are described for computing the coefficient matrices of the equations from a given equation of state.

Key words: nonlinear elasticity theory, symmetric hyperbolic equations, equations in Eulerian and Lagrangian coordinates, review.

Full text: PDF file (1904 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 975–995

Bibliographic databases:

UDC: 519.633
Received: 10.12.2007

Citation: S. K. Godunov, I. M. Peshkov, “Symmetric hyperbolic equations in the nonlinear elasticity theory”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 1034–1055; Comput. Math. Math. Phys., 48:6 (2008), 975–995

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. K. Godunov, I. M. Peshkov, “Symmetrization of the nonlinear system of gas dynamics equations”, Siberian Math. J., 49:5 (2008), 829–834  mathnet  crossref  mathscinet  isi  elib
    2. Peshkov I.M., “Numerical simulation of discontinuous solutions in nonlinear elasticity theory”, Journal of Applied Mechanics and Technical Physics, 50:5 (2009), 858–865  crossref  zmath  adsnasa  isi  isi  elib  scopus
    3. K. V. Brushlinskiǐ, V. G. Zhukov, M. K. Kerimov, “Academician SergeĭKonstantinovich Godunov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 50:1 (2010), 1–6  mathnet  crossref  mathscinet  adsnasa  isi  elib
    4. S. K. Godunov, I. M. Peshkov, “A thermodynamically consistent nonlinear model of an elastoplastic Maxwell medium”, Comput. Math. Math. Phys., 50:8 (2010), 1409–1426  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    5. V. A. Garanzha, “Polyconvex potentials, invertible deformations, and a thermodynamically consistent formulation of the equations of the nonlinear theory of elasticity”, Comput. Math. Math. Phys., 50:9 (2010), 1561–1587  mathnet  crossref  mathscinet  adsnasa  isi  elib
    6. Vshivkov V.A., Lazareva G.G., Snytnikov A.V., Kulikov I.M., Tutukov A.V., “Computational methods for ill-posed problems of gravitational gasodynamics”, J. Inverse Ill-Posed Probl., 19:1 (2011), 151–166  crossref  mathscinet  zmath  isi  elib  scopus
    7. V. M. Sadovskii, “Termodinamicheski samosoglasovannaya sistema zakonov sokhraneniya nesimmetrichnoi teorii uprugosti”, Dalnevost. matem. zhurn., 11:2 (2011), 201–212  mathnet
    8. E. I. Romenskii, “Termodinamicheski soglasovannaya sistema zakonov sokhraneniya techeniya szhimaemoi zhidkosti v poristoi uprugoi srede”, Sib. zhurn. industr. matem., 14:4 (2011), 86–97  mathnet  mathscinet
    9. Godunov S.K., “Thermodynamically consistent systems of hyperbolic equations”, Computational fluid dynamics 2010, 2011, 31–33  crossref  zmath  isi
    10. Vshivkov V.A., Lazareva G.G., Snytnikov A.V., Kulikov I.M., Tutukov A.V., “Hydrodynamical code for numerical simulation of the gas components of colliding galaxies”, Astrophysical Journal Supplement Series, 194:2 (2011), 47, 12 pp.  crossref  adsnasa  isi  scopus
    11. Gundlach C., Hawke I., Erickson S.J., “A conservation law formulation of nonlinear elasticity in general relativity”, Classical Quantum Gravity, 29:1 (2012), 015005, 53 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. S. K. Godunov, “Thermodynamic formalization of the fluid dynamics equations for a charged dielectric in an electromagnetic field”, Comput. Math. Math. Phys., 52:5 (2012), 787–799  mathnet  crossref  mathscinet  isi  elib  elib
    13. S. K. Godunov, S. P. Kiselev, I. M. Kulikov, V. I. Mali, “Numerical and experimental simulation of wave formation during explosion welding”, Proc. Steklov Inst. Math., 281 (2013), 12–26  mathnet  crossref  crossref  mathscinet  isi  elib
    14. S. K. Godunov, I. M. Kulikov, “Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee”, Comput. Math. Math. Phys., 54:6 (2014), 1012–1024  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    15. V. N. Belykh, K. V. Brushlinskii, V. L. Vaskevich, S. P. Kiselev, A. N. Kraiko, A. G. Kulikovskii, V. I. Mali, V. V. Pukhnachov, E. I. Romensky, V. S. Ryaben'kii, “Sergei Konstantinovich Godunov has turned 85 years old”, Russian Math. Surveys, 70:3 (2015), 561–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. M. A. Guzev, I. A. Molotkov, “Prodolnaya volna konechnoi amplitudy v nelineinoi odnorodnoi uprugoi srede. Uravneniya Landau – Murnagana”, Dalnevost. matem. zhurn., 16:2 (2016), 160–168  mathnet  elib
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