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Hyperbolic equations of Maxwell's nonlinear model of elastoplastic heat-conducting media

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Literature Cited

  1. S. K. Godunov and E. I. Romenskii, “Nonstationary equations of nonlinear elasticity theory in Euler coordinates,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 124–144 (1972).

    Google Scholar 

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

    Google Scholar 

  3. V. N. Dorovskii, A. M. Iskol'dskii, and E. I. Romenskii, “Dynamics of impulse heating of metals by current and electrical explosion of conductors,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 10–25 (1983).

    Google Scholar 

  4. L. A. Merzhievskii and A. D. Resnyanskii “Numerical modeling of deformation and destruction of hollow conic surfaces,” Fiz. Gor. Vzryva, No. 2, 102–110 (1987).

    Google Scholar 

  5. V. I. Kondaurov, “Relaxation-type equations for viscoelastic media with finite deformations,” Prikl. Mat. Mekh.,49, No. 5, 791–800 (1985).

    Google Scholar 

  6. A. L. Ni and V. E. Fortov, “Divergent system of nonstationary equations of motion of viscoelastic media in Euler coordinates,” Prikl. Mat. Mekh.,51, No. 6, 984–988 (1987).

    Google Scholar 

  7. E. I. Romenskii, “The dynamical three-dimensional equations of the elastoplastic model by H. A. Rahmatulin,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 138–158 (1979).

    Google Scholar 

  8. V. I. Kondaurov, “On conservation laws and symmetrization of equations of the nonlinear theory of thermoelasticity,” Dokl. Akad. Nauk SSSR,256, No. 4, 819–823 (1981).

    Google Scholar 

  9. E. I. Romenskii, “Conservation laws and the symmetric form of equations of nonlinear elasticity theory,” Boundary Value Problems for Partial Differential Equations, Proc. Sobolev Sem., Akad. Nauk SSSR, Sib. Otd., Inst. Mat., Novosibirsk No. 1, 132–143 (1984).

    Google Scholar 

  10. B. D. Coleman, M. Fabrizio, and D. R. Owen, “On the thermodynamics of second sound in dielectric crystals,” Arch. Ration. Mech. Anal.,80, No. 2, 135–158 (1982).

    Google Scholar 

  11. A. N. Malyshev and E. I. Romenskii, “Hyperbolic equations of heat conduction. Global solvability of the Cauchy problem,” Sib. Mat. Zh.,27, No. 5, 128–134 (1986).

    Google Scholar 

  12. B. D. Coleman, W. J. Hrusa, and D. R. Owen, “Stability of equilibrium for a nonlinear hyperbolic system describing heat propagation by second sound in solids,” Arch. Ration. Mech. Anal.,94, No. 3, 267–289 (1986).

    Google Scholar 

  13. F. Bampi and D. Fusco, “Nonlinear wave analysis of hyperbolic model of heat conduction,” Atti Sem. Mat. Fiz. Univ. Moderna,36, 197–209 (1988).

    Google Scholar 

  14. A. M. Iskol'dskii and E. I. Romenskii, “Dynamic model of thermoelastic continua with relaxation of pressure,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 132–138 (1984).

    Google Scholar 

  15. S. R. deGroot and P. Mazur, Nonequilibrium Thermodynamics, American Elsevier, New York (1962).

    Google Scholar 

  16. F. D. Murnaghan, Finite Deformation of an Elastic Solid, John Wiley, Chapman, New York (1951).

    Google Scholar 

  17. E. I. Romenskii, “Hyperelastic form of equations of nonlinear elasticity theory,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 133–138 (1974).

    Google Scholar 

  18. T. Kato, “The Cauchy problem for quasilinaer symmetric hyperbolic systems,” Arch. Ration. Mech. Anal.,58, No. 3, 181–205 (1975).

    Google Scholar 

  19. E. I. Romenskii, “Godunov's difference method for one-dimensional relaxational equations of thermoelastoplasticity,” Tr. Inst. Mat. Akad. Nauk SSSR, Sib. Otd.,11, 101–115 (1988).

    Google Scholar 

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Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 135–159, July–August, 1989.

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Romenskii, E.I. Hyperbolic equations of Maxwell's nonlinear model of elastoplastic heat-conducting media. Sib Math J 30, 606–625 (1989). https://doi.org/10.1007/BF00971761

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  • DOI: https://doi.org/10.1007/BF00971761

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