Large-time behavior of solutions to the equations of one-dimensional nonlinear thermoviscoelasticity
Authors:
L. Hsiao and Tao Luo
Journal:
Quart. Appl. Math. 56 (1998), 201-219
MSC:
Primary 73F15; Secondary 35B40, 35Q72, 45K05, 73B30
DOI:
https://doi.org/10.1090/qam/1622554
MathSciNet review:
MR1622554
Full-text PDF Free Access
References |
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Additional Information
- G. Andrews and J. M. Ball, Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity, J. Differential Equations 44 (1982), no. 2, 306–341. Special issue dedicated to J. P. LaSalle. MR 657784, DOI https://doi.org/10.1016/0022-0396%2882%2990019-5
- C. M. Dafermos, Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. Math. Anal. 13 (1982), no. 3, 397–408. MR 653464, DOI https://doi.org/10.1137/0513029
- C. M. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity, Nonlinear Anal. 6 (1982), no. 5, 435–454. MR 661710, DOI https://doi.org/10.1016/0362-546X%2882%2990058-X
- J. M. Greenberg and R. C. MacCamy, On the exponential stability of solutions of $E(u_{x})u_{xx}+\lambda u_{xtx}=\rho u_{tt}$, J. Math. Anal. Appl. 31 (1970), 406–417. MR 273178, DOI https://doi.org/10.1016/0022-247X%2870%2990034-X
- Takeyuki Nagasawa, On the one-dimensional motion of the polytropic ideal gas nonfixed on the boundary, J. Differential Equations 65 (1986), no. 1, 49–67. MR 859472, DOI https://doi.org/10.1016/0022-0396%2886%2990041-0
- Mari Okada and Shuichi Kawashima, On the equations of one-dimensional motion of compressible viscous fluids, J. Math. Kyoto Univ. 23 (1983), no. 1, 55–71. MR 692729, DOI https://doi.org/10.1215/kjm/1250521610
- L. Tartar, Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, Boston, Mass.-London, 1979, pp. 136–212. MR 584398
G. Andrews and J. M. Ball, Asymptotic behavior and changes of phase in one-dimensional nonlinear viscoelasticity, J. Differential Equations 44, 306–341 (1982)
C. M. Dafermos, Global smooth solutions to the initial boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. Math. Anal. 13, 397–408 (1982)
C. M. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity, Nonlinear Anal. T.M.A. 6, 435–454 (1982)
J. M. Greenberg and R. C. MacCamy, On the exponential stability of solutions of $E\left ( {u_x} \right ){u_{xx}} + \\ \lambda {u_{xtx}} = \rho {u_{tt}}$, J. Math. Appl. 31, 406–417 (1970)
T. Nagasawa, On the one-dimensional motion of polytropic ideal gas non-fixed on the boundary, J. Differential Equations 65, No. 1, 49–67 (1986)
M. Okada and S. Kawashima, On the equation of one-dimensional motion of compressible viscous fluids, J. Math. Kyoto Univ. 23, 55–71 (1983)
L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. IV, pp. 136–212, Research Notes in Math., Vol. 39, Pitman, Boston, London, 1979
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Article copyright:
© Copyright 1998
American Mathematical Society
