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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 13
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Articles

On the porous thermoelastic system with Coleman–Gurtin law

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Pages 4432-4452 | Received 27 May 2019, Accepted 29 Nov 2020, Published online: 11 Dec 2020

References

  • Nunziato JW, Cowin SC. A nonlinear theory of elastic materials with voids. Arch Ration Mec Anal. 1979;72:175–201.
  • Santos ML, Campelo ADS, Oliveira MLS. On porous-elastic systems with Fourier law. Appl Anal. 2019;98(6):1181–1197. DOI:10.1080/00036811.2017.1419197
  • Magaña A, Quintanilla R. On the time decay of solutions in one-dimensional theories of porous materials. Int J Solids Struct. 2006;43:3414–3427. DOI:10.1016/j.ijsolstr.2005.06.077
  • Santos ML, Campelo ADS, Almeida Júnior DS. On the decay rates of porous elastic systems. J Elast. 2017;127:79–101. DOI:10.1007/s10659-016-9597-y
  • Casas PS, Quintanilla R. Exponential decay in one–dimensional porous-thermo-elasticity. Mech Res Commun. 2005;32:652–659.
  • Soufyane A. Energy decay for porous-thermo-elasticity systems of memory type. Appl Anal. 2008;87:451–464.
  • Soufyane A, Afilal M, Chacha M. General decay of solutions of a linear one-dimensional porous-thermoelasticity system with a boundary control of memory type. Nonlinear Anal Theor, Meth Appl. 2010;72:3903–3910.
  • Soufyane A, Afilal M, Chacha M. Boundary stabilization of memory type for the porous-thermo-elasticity system. Abstr Appl Anal. 2009;0:1–17. DOI: 10.1155/2009/280790
  • Santos ML, Almeida Júnior DS. On porous-elastic system with localized damping. Z Angew Math Phys. 2016;67(63):1–18. DOI:10.1007/s00033-016-0622-6
  • Rivera JM, Quintanilla R. On the time polynomial decay in elastic solids with voids. J Math Anal Appl. 2008;338:1296–1309. DOI:10.1016/j.jmaa.2007.06.005
  • Feng B. On a semilinear Timoshenko–Coleman–Gurtin system: quasi-stability and attractors. Discrete Contin Dyn Syst. 2017;37(9):4729–4751. DOI:10.3934/dcds.2017203
  • Dell'Oroa F, Pata V. On the stability of Timoshenko systems with Gurtin–Pipkin thermal law. J Differ Equ. 2014;257:523–548.
  • Chepyzhov VV, Mainini E, Pata V. Stability of abstract linear semigroups arising from heat conduction with memory. Asymptotic Anal. 2006;50(3,4):269–291.
  • Dafermos CM. Asymptotic stability in viscoelasticity. Arch Rational Mech Anal. 1970;37:297–308.
  • Grasselli M, Pata V. Uniform attractors of nonautonomous dynamical systems with memory. Basel/Switzerland: Birkhauser Verlag; 2002. 155–178. (Progress in Nonlinear Differential Equations and Their Applications; 50).
  • Raposo CA, Apalara TA, Ribeiro JO. Analyticity to transmission problem with delay in porous-elasticity. J Math Anal Appl. 2018;466:819–834. DOI:10.1016/j.jmaa.2018.06.017
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag; 1983.
  • Santos ML, Soufyane A, Almeida Júnior DS. Asymptotic behavior to Bresse system with past history. Quart Appl Math. 2015;73:23–54.
  • Giorgi C, Naso MG, Pata V. Exponential stability in linear heat conduction with memory: a semigroup approach. Comm Appl Anal. 2001;5:121–134.
  • Prüss J. On the spectrum of C0-semigroups. Trans. AMS. 1984;28:847–857.
  • Liu Z, Zheng S. Semigroups associated with dissipative systems. Boca Raton, FL: Chapman & Hall/CRC; 1999. (Chapman & Hall/CRC Research Notes in Mathematics; 398).
  • Borichev A, Tomilov Y. Optimal polynomial decay of functions and operator semigroups. Math Ann. 2010;347(2):455–478.

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