On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound
Author:
Michael A. Tarabek
Journal:
Quart. Appl. Math. 50 (1992), 727-742
MSC:
Primary 73B30; Secondary 35Q72, 73C50
DOI:
https://doi.org/10.1090/qam/1193663
MathSciNet review:
MR1193663
Full-text PDF Free Access
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Additional Information
- Carlo Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3 (1949), 83–101 (Italian). MR 0032898
D. S. Chandrasekharaiah, Thermoelasticity with second sound: a review, Appl. Mech. Rev. 39, 355–376 (1986)
P. J. Chen and M. E. Gurtin, On second sound in materials with memory, Z. Angew. Math. Phys. 21, 232–241 (1970)
- Bernard D. Coleman, Mauro Fabrizio, and David R. Owen, On the thermodynamics of second sound in dielectric crystals, Arch. Rational Mech. Anal. 80 (1982), no. 2, 135–158. MR 666429, DOI https://doi.org/10.1007/BF00250739
- Bernard D. Coleman, Mauro Fabrizio, and David R. Owen, Second sound in crystals: thermodynamics and constitutive equations, Rend. Sem. Mat. Univ. Padova 68 (1982), 207–227 (1983) (Italian, with English summary). MR 702156
- Bernard D. Coleman and Victor J. Mizel, Thermodynamics and departures from Fourier’s law of heat conduction, Arch. Rational Mech. Anal. 13 (1963), 245–261. MR 151119, DOI https://doi.org/10.1007/BF01262695
- Bernard D. Coleman and Walter Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13 (1963), 167–178. MR 153153, DOI https://doi.org/10.1007/BF01262690
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N. Fox, Generalized thermoelasticity, Internat. J. Engrg. Sci. 7, 437–445 (1968)
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C. Cattaneo, Sulla coduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)
D. S. Chandrasekharaiah, Thermoelasticity with second sound: a review, Appl. Mech. Rev. 39, 355–376 (1986)
P. J. Chen and M. E. Gurtin, On second sound in materials with memory, Z. Angew. Math. Phys. 21, 232–241 (1970)
B. D. Coleman, M. Fabrizio, and D. R. Owen, On the thermodynamics of second sound in dielectric solids, Arch. Rat. Mech. Anal. 80, 135–158 (1982)
B. D. Coleman, M. Fabrizio, and D. R. Owen, Il secundo suono nei cristalli: termodinamica ed equazioni costitutive, Rend. Sem. Mat. Univ. Padova 68, 208–277 (1982)
B. D. Coleman and V. J. Mizel, Thermodynamics and departures from Fourier’s law of heat conduction, Arch. Rat. Mech. Anal. 13, 245–261 (1963)
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rat. Mech. Anal. 13, 167–178 (1963)
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. Rat. Mech. Anal. 94, 267–289 (1986)
W. A. Day, The Thermodynamics of Simple Materials with Fading Memory, Springer-Verlag, Berlin, 1970
N. Fox, Generalized thermoelasticity, Internat. J. Engrg. Sci. 7, 437–445 (1968)
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rat. Mech. Anal. 31, 113–126 (1968)
W. J. Hrusa and M. A. Tarabek, On smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity, Quart. Appl. Math. 47, 631–644 (1989)
T. J. R. Hughes, T. Kato, and J. E. Marsden, Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rat. Mech. Anal. 63, 273–294 (1977)
D. D. Joseph and L. Preziosi, Heat waves, Rev. Modern Phys. 61, 41–73 (1989)
P. D. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys. 5, 611–613 (1964)
R. C. MacCamy and V.J. Mizel, Existence and non-existence in the large of solutions of quasilinear wave equations, Arch. Rat. Mech. Anal. 25, 299–320 (1967)
I. Müller, The coldness, a universal function in thermoelastic bodies, Arch. Rat. Mech. Anal. 4, 319–332 (1971)
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Article copyright:
© Copyright 1992
American Mathematical Society