Literature Cited
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).
S. K. Godunov, Elements of Continuum Mechanics [in Russian], Nauka, Moscow (1978).
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).
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).
V. I. Kondaurov, “Relaxation-type equations for viscoelastic media with finite deformations,” Prikl. Mat. Mekh.,49, No. 5, 791–800 (1985).
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).
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).
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).
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).
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).
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).
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).
F. Bampi and D. Fusco, “Nonlinear wave analysis of hyperbolic model of heat conduction,” Atti Sem. Mat. Fiz. Univ. Moderna,36, 197–209 (1988).
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).
S. R. deGroot and P. Mazur, Nonequilibrium Thermodynamics, American Elsevier, New York (1962).
F. D. Murnaghan, Finite Deformation of an Elastic Solid, John Wiley, Chapman, New York (1951).
E. I. Romenskii, “Hyperelastic form of equations of nonlinear elasticity theory,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 133–138 (1974).
T. Kato, “The Cauchy problem for quasilinaer symmetric hyperbolic systems,” Arch. Ration. Mech. Anal.,58, No. 3, 181–205 (1975).
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).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 135–159, July–August, 1989.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971761