In this paper we consider three particular systems of the isothermal viscoelasticity with voids. Our main aim is to see how the coupling terms in the dissipative parts can be used to obtain qualitative properties which are not satisfied when the coupling terms are not present.
CowinSCNunziatoJW. Linear elastic materials with voids. J Elasticity1983; 13: 125–147.
2.
CowinSC. The viscoelastic behavior of linear elastic materials with voids. J Elasticity1985; 15: 185–191.
3.
NunziatoJWCowinSC. A nonlinear theory of elastic materials with voids. Arch Rational Mech Anal1979; 72: 175–201.
4.
IeşanD. Thermoelastic Models of Continua. Berlin: Springer, 2004.
5.
QuintanillaR. Slow decay for one-dimensional porous dissipation elasticity. Appl Math Lett2003; 16: 487–491.
6.
CasasPSQuintanillaR. Exponential stability in thermoelasticity with microtemperatures. Int J Engng Sci2005; 43: 33–47.
7.
CasasPSQuintanillaR. Exponential decay in one-dimensional porous-themoelasticity. Mech Res Commun2005: 32: 652–658.
8.
GlowinskiPLadaA. Stabilization of elasticity-viscoporosity system by linear boundary feedback. Math Meth Appl Sci2009; 32: 702–722.
9.
LazzariBNibbiR. On the influence of a dissipative boundary on the energy decay for a porous elastic solid. Mech Res Commun2009; 36: 581–586.
10.
MagañaAQuintanillaR. On the time decay of solutions in one-dimensional theories of porous materials. Int J Solids Structures2006; 43: 3414–3427.
11.
MuñozRiveraJEQuintanillaR. On the time polynomial decay in elastic solids with voids. J Math Anal Appl2008; 338: 1296–1309.
12.
HanZ-JXuGQ. Exponential decay in non-uniform porous-thermoe-elasticity model of Lord–Shulman type. Discrete Continuous Dynam Syst B2012; 17: 57–77.
13.
MessaoudiSAFarehA. General decay for a porous thermoelastic system with memory: The case of equal speeds. Nonlin Anal2011; 74: 6895–6906.
14.
PamplonaPXMuñoz RiveraJEQuintanillaR. On the decay of solutions for porous-elastic systems with historyJ Math Anal Appl2011; 379: 682–705.
15.
SoufyaneA. Energy decay for Porous-thermo-elasticity systems of memory type. Applicable Anal2008; 87: 451–464.
16.
NicasiseSValeinJ. Stabilization of non-homogeneous elastic materials with voids. J Math Anal Appl2012; 387: 1061–1087.
17.
LeseduarteMCMagañaAQuintanillaR. On the time decay of solutions in porous-thermo-elasticity of type II. Discrete Continuous Dynam Syst B2010; 13: 375–391.
18.
PamplonaPXMuñoz RiveraJEQuintanillaR. Stabilization in elastic solids with voids. J Math Anal Appl2009; 350: 37–49.
19.
PamplonaPXMuñoz RiveraJEQuintanillaR. Analyticity in porous-thermoelasticity with microtemperatures. J Math Anal Appl2012; 394: 645–655.
20.
IeşanDQuintanillaR. A theory of porous thermoviscoelastic mixtures. J Thermal Stresses2007; 30: 693–714.
21.
IeşanD. On a theory of thermoviscoelastic materials with voids. J Elasticity2011; 104: 369–384.
22.
PamplonaPXMuñoz RiveraJEQuintanillaR. On uniqueness and analyticity in thermoviscoelastic solids with voids. J Appl Anal Comput2011; 1: 251–266.
23.
KolodnerII. Existence of Longitudinal Waves in Anisotropic MediaJ Acoust Soc Am1966; 40: 730–731.
24.
ForteSVianelloM. Symmetry classes for elasticity tensors. J Elasticity1996; 43: 81–108.
25.
LiuZZhengS. Semigroups Associated to Dissipative Systems (Research Notes in Mathematics, vol. 398). Boca Raton, FL: Chapman & Hall/CRC, 1999.
26.
LiuZRenardyM. A note on the equation of a thermoelastic plate. Appl Math Lett1995; 8: 1–6.
