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Asymptotic behaviour of solutions of mixed problem for linear thermoelastic systems with microtemperatures and microstretch. (English) Zbl 1513.35397

Summary: In this paper, we study the mixed problem with dissipative boundary conditions for linear thermoelastic system with microtemperatures. We investigate the correctness of the mixed problem and set the exponential decay of the energy norm of solutions.

MSC:

35M10 PDEs of mixed type
35M33 Initial-boundary value problems for mixed-type systems of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
74A15 Thermodynamics in solid mechanics

References:

[1] Adams R.A.: Sobolev Spaces, Academic Press, New York, (1975). · Zbl 0314.46030
[2] Evans L.C.: Partial differential equations, 2nd ed., Graduate Studies in Mathematics, 19 749 (2010). · Zbl 1194.35001
[3] Eringen, A.C.: Linear theory of micropolar elasticity, J. Math. Mech., 15(6), 909-923 (1966). · Zbl 0145.21302
[4] Eringen A.C.: Microcontinuum Field Theories, Springer, Berlin, (1999). · Zbl 0953.74002
[5] Grot R.: Thermodynamics of a continuum with microstructure, Internat. J. Engrg. Sci. 7, 801-814 (1969). · Zbl 0185.53902
[6] Iesan D.: On a theory of micromorphic elastic solids with microtemperatures, J. Thermal Stresses 24(8), 737-752 (2001).
[7] Iesan D., Quintanilla R.: On the theory of thermoelasticity with microtemperatures, J. Thermal Stresses 23(3), 199-215 (2000).
[8] Komornik V.: Decay estimates for the wave equation with internal damping, Interna-tional Series Num. Math. Birkhauser Verlag Basel, 8, 253-266 (1994). · Zbl 0810.35064
[9] Racke, R.: Thermoelasticity with second sound -exponential stability in linear and non-linear 1-d, Math. Methods Appl. Sci., 25(5), 409-441 (2002). · Zbl 1008.74027
[10] Racke R.: Asymptotic behaviour of solutions in linear 2-or 3-d thermoelasticity with second sound, Quart. Appl. Math. 61(2), 315-328 (2003). · Zbl 1030.74018
[11] Wang Y.G.: Microlocal analysis in nonlinear thermoelasticity, Nonlinear Anal. 54(4), 683-705 (2003). · Zbl 1027.35007
[12] Wang Y.G., Reissig M.: Parabolic type decay rates for 1-D-thermoelastic systems with time-dependent coefficients, Monatsh. Math., 138(3), 239-259 (2003). · Zbl 1031.35145
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