References
- Goodman M, Cowin S. A continuum theory for granular materials. Arch Ration Mech Anal. 1972;44:249–266. doi: https://doi.org/10.1007/BF00284326
- Nunziato J, Cowin S. A nonlinear theory of elastic materials with voids. Arch Ration Mech Anal. 1979;72:175–201. doi: https://doi.org/10.1007/BF00249363
- 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: https://doi.org/10.1016/j.ijsolstr.2005.06.077
- Liu Z, Zheng S. Semigroups associated with dissipative systems. Boca Raton (FL): Chapman & Hall/CRC;; 1999. (Chapman & Hall/CRC research notes in mathematics; 398).
- Santos ML, Campelo ADS, Almeida Jùnior DS. Rates of decay for porous elastic system weakly dissipative. Acta Appl Math. 2017;151:1–16. DOI:https://doi.org/10.1007/s10440-017-0100-y.
- Santos ML, Campelo ADS, Almeida Jùnior DS. On the decay rates of porous elastic systems. J Elast. 2017;127:79–101. doi: https://doi.org/10.1007/s10659-016-9597-y
- Malacarne A, Muñoz-Rivera JE. Lack of exponential stability to Timoshenko system with viscoelastic Kelvin–Voigt type. Z Angew Math Phys. 2016;67(67):1–10. DOI:https://doi.org/10.1007/s00033-016-0664-9.
- Casas PS, Quintanilla R. Exponential decay in one-dimensional porous-thermo-elasticity. Mech Res Commun. 2005;32(6):652–659. doi: https://doi.org/10.1016/j.mechrescom.2005.02.015
- Santos ML, Almeida Jùunior DS. On porous-elastic system with localized damping. Z Angew Math Phys. 2016;67(63):1–18. DOI:https://doi.org/10.1007/s00033-016-0622-6.
- Santos ML, Campelo ADS, Oliveira MLS. On porous-elastic systems with Fourier law. Appl Anal Taylor Francis. 2018;98:1181–1197.
- Muñoz-Rivera JE, Quintanilla R. On the time polynomial decay in elastic solids with voids. J Math Anal Appl. 2008;338:1296–1309. doi: https://doi.org/10.1016/j.jmaa.2007.06.005
- Prüss J. On the spectrum of C 0–semigroups. Trans AMS. 1984;28:847–857. doi: https://doi.org/10.2307/1999112
- Gearhart L. Spectral theory for contraction semigroups on Hilbert spaces. Trans AMS. 1978;236:385–394. doi: https://doi.org/10.1090/S0002-9947-1978-0461206-1
- Borichev A, Tomilov Y. Optimal polynomial decay of functions and operator semigroups. Math Ann. 2010;347:455–478. doi: https://doi.org/10.1007/s00208-009-0439-0