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References
Adams, R.A.: Sobolev spaces. Academic Press; New York (1975)
Carlson, D.E.: Linear thermoelasticity. Handbuch der Physik VIa/2. Springer-Verlag; Berlin, Heidelberg, New York (1972), 297–345.
Dafermos, C.M.: On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity. Arch. Rat. Mech. Anal. 29 (1968), 241–271.
Dafermos, C.M.: Dissipation, stabilization and the second law of thermodynamics. Lec. Notes Phys. 228 (1984), 44–88.
Dafermos, C.M. & Hsiao, L.: Development of singularities in solutions of the equations of nonlinear thermoelasticity. Quart. Appl. Math. 44 (1986), 463–474.
Dassios, G. & Grillakis, M.: Dissipation rates and partition of energy in thermoelasticity. Arch. Rat. Mech. Anal. 87 (1984), 49–91.
Gilliam, D.S. & Schulenberger, J.R.: Electromagnetic waves in a three-dimensional half-space with a dissipative boundary. J. Math. Anal. Appl. 89 (1982), 129–185.
Kawashima, S.: Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics. Thesis; Kyoto University (1983).
Klainerman, S. & Majda, A.: Formation of singularities for wave equations including the nonlinear vibrating string. Comm. Pure Appl. Math. 33 (1980), 241–263.
Kowalski, T. & Piskorek, A.: Existenz der Lösung einer Anfangsrandwertaufgabe in der linearen Thermoelastizitätstheorie. ZAMM 61 (1981), T250–T252.
Kupradze, V.D.: Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. North-Holland; Amsterdam (1979).
Leis, R.: Außenraumaufgaben in der linearen Thermoelastizitätstheorie. Math. Meth. in the Appl. Sci. 2 (1980), 379–396.
Leis, R.: Über das asymptotische Verhalten thermoelastischer Wellen im ”3. Math. Meth. in the Appl. Sci. 3 (1981), 312–317.
Leis, R.: Initial boundary value problems in mathematical physics. B.G. Teubner; Stuttgart. John Wiley & Sons; Chichester et al. (1986).
MacCamy, R.C. & Mizel, V.J.: Existence and non-existence in the large of solutions of quasi-linear wave equations. Arch. Rat. Mech. Anal. 25 (1967), 299–320.
Mochizuki, K.: Spectral and scattering theory for symmetric hyperbolic systems in an exterior domain. Publ. RIMS, Kyoto Univ., Vol. 5 (1969), 219–258.
Racke, R.: On the time-asymptotic behaviour of solutions in thermoelasticity. Proc. Roy. Soc. Edinburgh 107A (1987), 289–298
Racke, R.: Eigenfunction expansions in thermoelasticity. J. Math. Anal. Appl. 120 (1986), 596–609.
Racke, R.: Uniqueness of weak solutions in linear thermoelasticity. Bull. Pol. Ac. Sci., Tech. Sci. 34, No. 11–12 (1986), 613–620.
Racke, R.: Initial boundary value problems in one-dimensional non-linear thermoelasticity. Submitted to: Math. Meth. Appl. Sci..
Slemrod, M.: Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity. Arch. Rat. Mech. Anal. 76 (1981), 97–134.
Smoller, J.: Shock waves and reaction-diffusion equations. Springer-Verlag New York, Heidelberg, Berlin (1983).
Wloka, J.: Partielle Differentialgleichungen. B.G. Teubner; Stuttgart (1982).
Zheng, S.: Global solutions and applications to a class of quasilinear hyperbolic-parabolic coupled systems. Scienta Sinica Ser. A 27 (1984), 1274–1286.
Zheng, S.: Initial boundary value problems for quasilinear hyperbolic-parabolic coupled systems in higher dimensional spaces. Chin. Ann. of Math. 4B(4) (1983), 443–462.
Zheng, S. & Shen, W.: Global solutions to the Cauchy problem of a class of quasilinear hyperbolic parabolic coupled systems. To appear in: Scienta Sinica.
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Racke, R. (1988). Initial boundary value problems in thermoelasticity. In: Hildebrandt, S., Leis, R. (eds) Partial Differential Equations and Calculus of Variations. Lecture Notes in Mathematics, vol 1357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082874
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DOI: https://doi.org/10.1007/BFb0082874
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