Global large solutions to initial-boundary value problems in one-dimensional nonlinear thermoviscoelasticity
Author:
Song Jiang
Journal:
Quart. Appl. Math. 51 (1993), 731-744
MSC:
Primary 35Q72; Secondary 73B30, 73F15
DOI:
https://doi.org/10.1090/qam/1247437
MathSciNet review:
MR1247437
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Abstract: Initial boundary value problems in one-dimensional nonlinear thermo-viscoelasticity are considered, and the existence of global classical solutions is established by means of the Leray-Schauder fixed point theorem.
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A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964
S. Kawashima and T. Nishida, Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gases, J. Math. Kyoto Univ. 21, 825–837 (1981)
B. Kawohl, Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting, one-dimensional real gas, J. Differential Equations 58, 76–103 (1985)
A. V. Kazhykhov, Sur la solubilité globale des problémes monodimensionnels aux valeurs initialeslimitées pour les équations d’un gaz visqueux et calorifére, C. R. Acad. Sci. Paris Sér. A 284, 317–320 (1977)
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech. 41, 273–282 (1977)
J. U. Kim, Global existence of solutions of the equations of one-dimensional thermoviscoelasticity with initial data in BV and $L^{1}$ , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 10, 357–427 (1983)
O. A. Ladyzenskaya, V. A. Solonnikov, and N. N. Uraĺceva, Linear and Quasilinear Equations of Parabolic Type, transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968
T. Nagasawa, On the one-dimensional motion of the polytropic ideal gas nonfixed on the boundary, J. Differential Equations 65, 49–67 (1986)
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T. Nishida, Equations of motion of compressible viscous fluids, Patterns and Waves—Qualitative Analysis of Nonlinear Differential Equations (T. Nishida, M. Mimura, and H. Fujii, eds.), Kinokuniya/North-Holland, Tokyo/Amsterdam, 1986
M. Okada and S. Kawashima, On the equations of one-dimensional motion of compressible viscous fluids, J. Math. Kyoto Univ. 23, 55–71 (1983)
M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967
S. Zheng and W. Shen, Global smooth solutions to the Cauchy problem of equations of one-dimensional nonlinear thermoviscoelasticity, J. Partial Differential Equations 2, 26–38 (1989)
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Article copyright:
© Copyright 1993
American Mathematical Society
