On the stabilization of linear porous elastic materials by microtemperature effect and porous damping

Goodman, M.A., Cowin, S.C.: A continuum theory for granular materials. Arch. Ration. Mech. Anal. 44(4), 249–266 (1972)

Ieşan, D., Quintanilla, R.: On a theory of thermoelasticity with microtemperatures. J. Therm. Stresses 23(3), 199–215 (2000)

Ieşan, D.: On a theory of micromorphic elastic solids with microtemperatures. J. Therm. Stresses 24(8), 737–752 (2001)

Ieşan, D.: Thermoelastic Models of Continua. Springer, Dordrecht (2004)

Ieşan, D., Quintanilla, R.: A theory of porous thermoviscoelastic mixtures. J. Therm. Stresses 30(7), 693–714 (2007)

Chiriţ a, S., Ciarletta, M., D’Apice, C.: On the theory of thermoelasticity with microtemperatures. J. Math. Anal. Appl. 397(1), 349–361 (2013)

Quintanilla, R.: Slow decay for one-dimensional porous dissipation elasticity. Appl. Math. Lett. 16(4), 487–491 (2003)

Casas, P.S., Quintanilla, R.: Exponential stability in thermoelasticity with microtemperatures. Int. J. Eng. Sci. 43(1–2), 33–47 (2005)

Liu, Z., Zheng, S.: Semigroups Associated with Dissipative Systems. Chapman and Hall, Boca Raton (1999)

Casas, P.S., Quintanilla, R.: Exponential decay in one-dimensional porous-thermo-elasticity. Mech. Res. Commun. 32(6), 652–658 (2005)

Magaña, A., Quintanilla, R.: On the time decay of solutions in one-dimensional theories of porous materials. Int. J. Solids Struct. 43(11–12), 3414–3427 (2006)

Apalara, T.A.: Exponential decay in one-dimensional porous dissipation elasticity. Q. J. Mech. Appl. Math. 70(4), 553–572 (2017)

Apalara, T.A.: General decay of solutions in one-dimensional porous-elastic system with memory. J. Math. Anal. Appl. 469, 457–471 (2017)

Fareh, A., Messaoudi, S.A.: Energy decay for a porous thermoelastic system with thermoelasticity of second sound and with a non-necessary positive definite energy. Appl. Math. Comput. 293, 493–507 (2017)

Muñoz Rivera, J.E., Quintanilla, R.: On the time polynomial decay in elastic solids with voids. J. Math. Anal. Appl. 338(2), 1296–1309 (2008)

Pamplona, P.X., Muñoz Rivera, J.E., Quintanilla, R.: Stabilization in elastic solids with voids. J. Math. Anal. Appl. 350(1), 37–49 (2009)

Pamplona, P.X., Muñoz Rivera, J.E., Quintanilla, R.: On the decay of solutions for porous-elastic systems with history. J. Math. Anal. Appl. 379(2), 682–705 (2011)

Santos, M.L., Junior, D.A.: On porous-elastic system with localized damping. Z. Angew. Math. Phys. 67(3), 1–18 (2016)

Santos, M.L., Campelo, A.D.S., Junior, D.A.: On the decay rates of porous elastic systems. J. Elast. 127(1), 79–101 (2017)

Santos, M.L., Junior, D.A.: On the porous-elastic system with Kelvin–Voigt damping. J. Math. Analy. Appl. 445(1), 498–512 (2017)

Soufyane, A.: Energy decay for porous-thermo-elasticity systems of memory type. Appl. Anal. 87(4), 451–464 (2008)

Soufyane, A., Afilal, M., Aouam, T., Chacha, M.: General decay of solutions of a linear one-dimensional porous-thermoelasticity system with a boundary control of memory type. Nonlinear Anal. 72(11), 3903–3910 (2010)

Hachelfi, M., Djebabla, A., Tatar, N.: On the decay of the energy for linear thermoelastic systems by thermal and micro-temperature effects. Eurasian J. Math. Comput. Appl. 6(2018), 29–37 (2018)

Apalara, T.A.: On the stability of porous-elastic system with microtemparatures. J. Therm. Stresses 42(2), 265–278 (2019)

Liu, Z., Zheng, S.: Semigroups associated with dissipative systems. In: Pitman Research Notes in Mathematics, vol. 398. Chapman and Hall, Boca Raton (1999)

Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)