Soufyane, Abdelaziz; Afilal, Mounir; Chacha, Mama Boundary stabilization of memory type for the porous-thermo-elasticity system. (English) Zbl 1165.74015 Abstr. Appl. Anal. 2009, Article ID 280790, 17 p. (2009). Summary: For a one-dimensional viscoelastic porous-thermo-elastic system, we establish general decay results. The usual exponential and polynomial decay rates are only special cases. Cited in 21 Documents MSC: 74F05 Thermal effects in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74D05 Linear constitutive equations for materials with memory Keywords:general decay rate; exponential decay rate; polynomial decay rate × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] M. Slemrod, “Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity,” Archive for Rational Mechanics and Analysis, vol. 76, no. 2, pp. 97-133, 1981. · Zbl 0481.73009 · doi:10.1007/BF00251248 [2] S. Jiang, “Global solutions of the Neumann problem in one-dimensional nonlinear thermoelasticity,” Nonlinear Analysis: Theory, Methods & Applications, vol. 19, no. 2, pp. 107-121, 1992. · Zbl 0786.73009 · doi:10.1016/0362-546X(92)90114-T [3] G. Lebeau and E. Zuazua, “Decay rates for the three-dimensional linear system of thermoelasticity,” Archive for Rational Mechanics and Analysis, vol. 148, no. 3, pp. 179-231, 1999. · Zbl 0939.74016 · doi:10.1007/s002050050160 [4] Z. Liu and S. Zheng, Semigroups Associated with Dissipative Systems, vol. 398 of Chapman &Hall/CRC Research Notes in Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 1999. · Zbl 0924.73003 [5] R. Racke, “Thermoelasticity with second sound-exponential stability in linear and non-linear 1-d,” Mathematical Methods in the Applied Sciences, vol. 25, no. 5, pp. 409-441, 2002. · Zbl 1008.74027 · doi:10.1002/mma.298 [6] X. Zhang and E. Zuazua, “Decay of solutions of the system of thermoelasticity of type III,” Communications in Contemporary Mathematics, vol. 5, no. 1, pp. 25-83, 2003. · Zbl 1136.74318 · doi:10.1142/S0219199703000896 [7] P. S. Casas and R. Quintanilla, “Exponential decay in one-dimensional porous-thermo-elasticity,” Mechanics Research Communications, vol. 32, no. 6, pp. 652-658, 2005. · Zbl 1192.74156 · doi:10.1016/j.mechrescom.2005.02.015 [8] R. Quintanilla, “Slow decay for one-dimensional porous dissipation elasticity,” Applied Mathematics Letters, vol. 16, no. 4, pp. 487-491, 2003. · Zbl 1040.74023 · doi:10.1016/S0893-9659(03)00025-9 [9] A. Soufyane, “Energy decay for porous-thermo-elasticity systems of memory type,” Applicable Analysis, vol. 87, no. 4, pp. 451-464, 2008. · Zbl 1135.74301 · doi:10.1080/00036810802035634 [10] P. X. Pamplona, J. E. Muñoz Rivera, and R. Quintanilla, “Stabilization in elastic solids with voids,” Journal of Mathematical Analysis and Applications, vol. 350, no. 1, pp. 37-49, 2009. · Zbl 1153.74016 · doi:10.1016/j.jmaa.2008.09.026 [11] M. M. Cavalcanti, V. N. Domingos Cavalcanti, and M. L. Santos, “Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary,” Applied Mathematics and Computation, vol. 150, no. 2, pp. 439-465, 2004. · Zbl 1047.35107 · doi:10.1016/S0096-3003(03)00284-4 [12] M. M. Cavalcanti and H. P. Oquendo, “Frictional versus viscoelastic damping in a semilinear wave equation,” SIAM Journal on Control and Optimization, vol. 42, no. 4, pp. 1310-1324, 2003. · Zbl 1053.35101 · doi:10.1137/S0363012902408010 [13] M. de Lima Santos, “Asymptotic behavior of solutions to wave equations with a memory condition at the boundary,” Electronic Journal of Differential Equations, vol. 2001, no. 73, pp. 1-11, 2001. · Zbl 0984.35025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.