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Media with equations of state that depend on derivatives

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References

  1. S. K. Godunov, “An interesting class of quasilinear systems,”Dokl. Akad. Nauk SSSR,139, No. 3, 521–523 (1961).

    MATH  MathSciNet  Google Scholar 

  2. S. K. Godunov, “Symmetric form of magnetic hydrodynamics,”Numerical Methods of Continuum Mechanics [in Russian], Inst. of Theor. and Appl. Mech., Sibirian Division, Academy of Sceince of the USSR,3, No. 1, 26–34 (1972).

    MATH  Google Scholar 

  3. S. K. Godunov,Elements of Continuum Mechanics [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. E. I. Romenskii, “Conservation laws and symmetric form of equations of the nonlinear theory of elasticity,” in:Boundary Value Problems for Partial Differential Equations [in Russian], Novosibirsk, No. 1, 132–134 (1984).

  5. A. M. Blokhin,Energy Integrals and Their Applications to Problems of Gasdynamics [in Russian], Nauka, Novosibirsk (1986).

    Google Scholar 

  6. A. M. Blokhin and V. N. Dorovskii,Problems of Mathematical Modeling in the Theory of Multi-Velocity Continuum [in Russian], Novosibirsk (1994).

  7. A. F. Voyevodin and S. M. Shugrin,Methods for Solving One-Dimensional Evolutionary Equations [in Russian], Nauka, Moscow (1993).

    Google Scholar 

  8. G. B. Whitham,Linear and Nonlinear Waves [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  9. R. L. Pego and M. J. Weinstein, “Eigenvalues and instabilities of solitary waves,”Philos. Trans. Roy. Soc. Lond. Ser A,340, 47–94 (1992).

    ADS  MathSciNet  Google Scholar 

  10. T. B. Benjamin, J. L. Bona, and J. J. Mahony, “Model equations for long waves in nonlinear dispersive systems,”Philos. Trans. Roy. Soc. Lond. Ser. A,272, 47–78 (1972).

    ADS  MathSciNet  Google Scholar 

  11. V. F. Nesterenko, “Examples of ‘sonic vacuum’,”Fiz. Goreniya Vzryva,29, No. 2, 132–134 (1993).

    MathSciNet  Google Scholar 

  12. S. L. Gavrilyuk and D. Serre, “A model of a plug-chain system near the thermodynamic critical point with the Korteweg theory of capillarity and modulation equations,” in: IUTAM Symposium on Waves in Liquid/Gas and Liquid/Vapour Two-Phase Systems, Kyoto, Japan, 1994. Kluwer, Dordrecht (1995), pp. 419–428.

    Google Scholar 

  13. V. F. Nesterenko, “Solitary waves in a discrete medium with anomalous compressibility,”Fiz. Goreniya Vzryva,29, No. 2, 134–136 (1993).

    MathSciNet  Google Scholar 

  14. M. Slemrod, “The viscosity-capillarity approach to phase transitions,” in:PDEs and Continuum Models of Phase Transitions, Springer Verlag, Berlin et al. (1989) (Lect. Not. in Phys.344).

    Google Scholar 

  15. H. Gouin and J.-F. Debieve, “Variational principle involving the stress tensor in elastodynamics,”Int. J. Eng. Sci.,24, No. 7, 1057–1066 (1986).

    Google Scholar 

  16. P. Casal and H. Gouin, “A representation of liquid-vapour interfaces by using fluids of second grade,”Ann. Phys. Suppl. 3,13, 3–12 (1988).

    Google Scholar 

  17. S. L. Gavrilyuk and V. F. Nesterenko, “Stability of periodic excitations for a model of ‘sonic vacuum’,”Prikl. Mekh. Tekh. Fiz.,34, No. 6, 45–48 (1993).

    Google Scholar 

  18. S. V. Iordanskii, “On equations of motion of a liquid containing gas bubbles,”Prikl. Mekh. Tekh. Fiz., No. 3, 102–110 (1960).

    MATH  Google Scholar 

  19. B. S. Kogarko, “One model of a cavitating liquid,”Dokl. Akad. Nauk SSSR,137, No. 6, 1331–1333 (1961).

    MathSciNet  Google Scholar 

  20. L. van Wijngaarden, “One-dimensional flow of liquids containing small gas bubbles,”Annu. Rev. Fluid Mech.,4, 369–396 (1972).

    Article  ADS  MATH  Google Scholar 

  21. S. L. Gavrilyuk, “Large-amplitude oscillations and their ‘thermodynamics’ for continua with ‘memory’,”Eur. J. Mech. B/Fluids,13, No. 6, 753–764 (1994).

    MATH  MathSciNet  Google Scholar 

  22. S. L. Gavrilyuk, “Modulation equations for a bubbly liquid with an incompressible carrier phase,”Prikl. Mekh. Tekh. Fiz., No. 2, 86–92 (1989).

    MathSciNet  Google Scholar 

  23. N. A. Gumerov, “Equations describing the propagation of nonlinear modulation waves in bubbly liquids,” in:Bubble Dynamics and Interphase Phenomena, Kluwer, Dordrecht (1994), pp. 131–140.

    Google Scholar 

  24. H. Gouin, “Utilization of the second gradient theory in continuum mechanics to study the motion and thermodynamics of liquid-vapour interfaces,” in:Interfacial Phenomena, Plenum Press, London (1987), pp. 667–682.

    Google Scholar 

  25. V. L. Berdichevskii,Variational Principles of Continuum Mechanics [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  26. P. G. Olver,Applications of Lie Groups to Differential Equations [Russian translation], Mir, Moscow (1989).

    Google Scholar 

  27. S. M. Shugrin, “Two-velocity hydrodynamics and thermodynamics,”Prikl. Mekh. Tekh. Fiz.,35, No. 4, 41–59 (1994).

    MATH  MathSciNet  Google Scholar 

  28. S. M. Shugrin, “Dissipative two-velocity hydrodynamics,”ibid.Prikl. Mekh. Tekh. Fiz.,35, No. 4, (1994), 59–68.

    MATH  MathSciNet  Google Scholar 

  29. P. Casal and H. Gouin, “Invariance properties of inviscid fluids of grade N,” in:PDEs and Continuum Models of Phase Transitions, Springer Verlag, Berlin (1989), pp. 85–98 (Lect. Not. in Phys.,344).

    Google Scholar 

  30. A. A. Atavin and S. M. Shugrin, “On differential equations of shallow water theory,” in:Dynamics of Continuous Media [in Russian], Institute of Hydrodynamics, Novosibirsk,70 (1985), pp. 25–53.

    Google Scholar 

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Levrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 37, No. 2, pp. 35–49, March–April, 1996.

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Gavrilyuk, S.L., Shugrin, S.M. Media with equations of state that depend on derivatives. J Appl Mech Tech Phys 37, 177–189 (1996). https://doi.org/10.1007/BF02382423

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