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Articles

Multidimensional thermoelasticity for nonsimple materials – well-posedness and long-time behavior

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Pages 1561-1585 | Received 06 May 2016, Accepted 11 Feb 2017, Published online: 28 Feb 2017

References

  • Truesdell C, Noll W. In: Antman SS, editor. The non-linear field theories of mechanics. 3rd ed., Berlin: Springer-Verlag; 2004.
  • Green AE, Naghdi PM. A unified procedure for construction of theories of deformable media I. Classical continuum physics, Proc Math Phys Eng Sci. 1934;1995(448):335–356.
  • Green AE, Naghdi PM. A unified procedure for construction of theories of deformable media II. Generalized continua, Proc Math Phys Eng Sci. 1934;1995(448):357–377.
  • Green AE, Naghdi PM. A unified procedure for construction of theories of deformable media III. Mixtures of interacting continua, Proc Math Phys Eng Sci. 1934;1995(448):379–388.
  • Rajagopal KR. On implicit constitutive theories. Appl Math. 2003;48:279–319.
  • Truesdell C, Toupin RA. The classical field theories. In: Flügge S, editor. Handbuch der Physik. Vol. III/1, Berlin: Springer-Verlag; 1960.
  • Green AE, Rivlin RS. Multipolar continuum mechanics. Arch Ration Mech An. 1964;17:113–147.
  • Mindlin RD. Micro-structure in linear elasticity. Arch Ration Mech An. 1964;16:51–78.
  • Toupin RA. Theorie of elasticity with couple-stress. Arch Ration Mech An. 1964;17:85–112.
  • Ciarletta M, Ieşan D. Non-classical elastic solids. Vol. 293, Pitman research notes in mathematical sciences. Harlow, Essex: Longman Scientific & Technical; 1993.
  • Ieşan D. Thermoelastic models of continua. Vol. 118. Solid mechanics and its applications. Dordrecht: Springer; 2004.
  • Quintanilla R. Thermoelasticity without dissipation of nonsimple materials. Z Angew Math Mech. 2003;83:172–180.
  • Marin M, Marinescu C. Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies. Int J Eng Sci. 1998;36(1):73–86.
  • Fernández Sare HD. Munñoz Rivera JE, Quintanilla R. Decay of solutions in nonsimple thermoelastic bars. Int J Eng Sci. 2010;48:1233–1241.
  • Magaña A, Quintanilla R. Exponential decay in nonsimple thermoelasticity of type III. Math Method Appl Sci. 2014;39:225–235.
  • Pata V, Quintanilla R. On the decay of solutions in nonsimple elastic solids with memory. J Math Anal Appl. 2010;363:19–28.
  • Gawinecki JA, Łazuka J. Global solution on Cauchy problem in nonlinear non-simple thermoelastic materials. Proc Appl Mat Mech. 2006;6:371–372.
  • Aouadi M, Moulahi T. Approximate controllability of abstract nonsimple thermoelastic problem. Evol Equ Contr Theor. 2015;4(4):373–389.
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. New York (NY): Springer; 1983.
  • Christov CI. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mech Res Commun. 2009;36(4):481–486.
  • Lasiecka I, Tataru D. Uniform boundary stabilization of semilineaer wave equation with nonlinear boundary damping. Differ Integral Equ. 1993;6:507–533.
  • Haraux A. Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugal Math. 1989;46:245–258.
  • Pokojovy M. On stability of hyperbolic thermoelastic Reissner-Mindlin-Timoshenko plates. Math Meth Appl Sci. 2015;38:1225–1246.
  • Marin M. Some basic theorems in elastostatics of micropolar materials with voids. J Comput Appl Math. 1996;70(1):115–126.
  • Liu Z, Zheng S. Semigroups associated with dissipative systems. Boca Raton, London, New York (NY), Washington (DC).: Chapman and Hall/CRC; 1999.
  • Tamma KK, Zhou X. Macroscale and microscale thermal transport and thermo-mechanical interactions: some noteworthy perspectives. J Therm Stresses. 1998;21(3–4):405–449.
  • Stone MH. On one-parameter unitary groups in Hilbert Space. Ann Math. 1932;33(3):643–648.
  • Tucsnak M, Weiss G. Observation and control for operator semigroups. Springer Science & Business Media. Birkhäuser: Basel, Boston, Berlin; 2009.
  • Tebou L. Equivalence between observability and stabilization for a class of second order semilinear evolution equations. Discret Contin Dyn Syst. 2009;1:744–752.
  • Kadets V. Kurs funkcionalnogo analiza (A course in functional analysis). Kharkiv: University of Kharkiv; 2006. Russian. ISBN 966-623-199-9.

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