Attractors for partially damped systems of binary mixtures of solids

References

• Atkin RJ, Craine RE. Continuum theories of mixtures basic theory and historical development. Q J Mech Appl Math. 1976;29:209–244.
   Web of Science ®Google Scholar
• Bedford A, Drumheller DS. Theories of immiscible and structured mixtures. Int J Eng Sci. 1983;21:863–960.
   Web of Science ®Google Scholar
• Klika V. A guide through available mixture theories for applications. Crit Rev Solid State Mater Sci. 2013;39:154–174.
   Web of Science ®Google Scholar
• Karaborni S, Smit B, Heidug W, et al. The swelling of clays: molecular simulations of the hydration of montmorillonite. Science. 1996;271:1102–1104.
   Web of Science ®Google Scholar
• Wray W. So your home is built on expansive soils. New York (NY): Amer Soc Civil Eng; 1995.
   Google Scholar
• Ieşan D. On the theory of mixtures of thermoelastic solids. J Therm Stress. 1991;14:389–408.
   Web of Science ®Google Scholar
• Quintanilla R. Exponential stability for one-dimensional problem of swelling porous elastic soils with fluid saturation. J Comput Appl Math. 2002;145:525–533.
   Web of Science ®Google Scholar
• Wang J-M, Guo B-Z. On the stability of swelling porous elastic soils with fluid saturation by one internal damping. IMA J Appl Math. 2006;71:565–582.
   Web of Science ®Google Scholar
• Ramos A, Almeida Júnior D, Freitas M, et al. Stabilization of swelling porous elastic soils with fluid saturation and delay time terms. J Math Phys. 2021;62:Article ID 021507.
   Web of Science ®Google Scholar
• Ramos A, Freitas M, Almeida D, Jr., et al. Stability results for elastic porous media swelling with nonlinear damping. J Math Phys. 2020;61:1–10.
   Web of Science ®Google Scholar
• Apalara TA. General stability result of swelling porous elastic soils with a viscoelastic damping. Z angew Math Phys. 2020;71:1–10.
   Web of Science ®Google Scholar
• Apalara TA, Yusuf MO, Salami BA. On the control of viscoelastic damped swelling porous elastic soils with internal delay feedbacks. J Math Anal Appl. 2021;504:125429.
   Web of Science ®Google Scholar
• Choucha A, Boulaaras SM, Ouchenane D, et al. Exponential stability of swelling porous elastic with a viscoelastic damping and distributed delay term. J Funct Spaces. 2021;2021:1–8.
   Web of Science ®Google Scholar
• Dell'Oro F, Muñoz Rivera JE. Stabilization of ternary mixtures with frictional dissipation. Asymptot Anal. 2014;89:235–262.
   Web of Science ®Google Scholar
• Quintanilla R. On the linear problem of swelling porous elastic soils with incompressible fluid. Int J Eng Sci. 2002;40:1485–1494.
   Web of Science ®Google Scholar
• Quintanilla R. Exponential stability of solutions of swelling porous elastic soils. Meccanica. 2004;39:139–145.
   Web of Science ®Google Scholar
• Feng B, Yang X-G. Long-time dynamics for a nonlinear timoshenko system with delay. Appl Anal. 2017;96:606–625.
   Web of Science ®Google Scholar
• Barbosa ARA, Ma TF. Long-time dynamics of an extensible plate equation with thermal memory. J Math Anal Appl. 2014;416:143–165.
   Web of Science ®Google Scholar
• Bocanegra-Rodriguez LE, Silva MAJ, Ma TF, et al. Longtime dynamics of a semilinear lamé system. J Dyn Differ Equ. 2021; https://doi.org/10.1007/s10884-021-09955-7.
   Web of Science ®Google Scholar
• Chueshov I, Lasiecka I. Long-time behavior of second order evolution equations with nonlinear damping. Providence: Memoirs of AMS 912, AMS; 2008.
   Google Scholar
• Dos Santos MJ, Feng B, Júnior DSA, et al. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete Cont Dyn Syst Ser B. 2021;26:2805.
   Web of Science ®Google Scholar
• Freitas MM, Costa ALC, Santos Araújo GM. Pullback dynamics of a non-autonomous mixture problem in one dimensional solids with nonlinear damping. Commun Pur Appl Math. 2020;19:785–809.
   Google Scholar
• Freitas MM, Ramos AJA, Almeida Júnior DS, et al. Global and exponential attractors for mixtures of solids with fourier's law. Nonlinear Anal Real World Appl. 2022;63:Article ID 103391.
   Web of Science ®Google Scholar
• Freitas MM, Ramos AJA, Santos ML. Existence and upper-semicontinuity of global attractors for binary mixtures solids with fractional damping. Appl Math Optim. 2021;83:1353–1385.
   Web of Science ®Google Scholar
• Santos ML, Freitas MM. Global attractors for a mixture problem in one dimensional solids with nonlinear damping and sources terms. Commun Pur Appl Math. 2019;18:1869–1890.
   Google Scholar
• Santos ML, Freitas MM, Ramos AJA. Blow-up result and energy decay rates for binary mixtures of solids with nonlinear damping and source terms. Nonlinear Anal Real World Appl. 2020;52:Article ID 103026.
   Web of Science ®Google Scholar
• Pazy A. Semigroups of linear operators and applications to partial differential equations. Berlin: Springer-Verlag; 1983.
   Google Scholar
• Zheng S. Nonlinear evolution equations. Boca Raton (FL): Chapman & Hall/ CRC Press; 2004. (Pitman ser monogr surv pure appl math; 133).
   Google Scholar
• Babin AV, Vishik MI. Attractors of evolution equations. Amsterdam: North Holland; 1992.
   Google Scholar
• Billotti JE, LaSalle JP. Dissipative periodic processes. Bull Amer Math Soc. 1971;77:1082–1088.
   Web of Science ®Google Scholar
• Chueshov I, Lasiecka I. Von Karman evolution equations. Well-posedness and long time dynamics. New York (NY): Springer; 2010. (Springer monographs in mathematics).
   Google Scholar
• Hale JK. Asymptotic behavior of dissipative systems. Providence (RI): American Mathematical Society; 1988. (Mathematical surveys and monographs).
   Google Scholar
• Ladyzhenskaya OA. Attractors for semigroups and evolution equations. Cambridge: Cambridge University Press; 1991.
   Google Scholar
• Robinson JC. Infinite-dimensional dynamical systems: an introduction to dissipative parabolic PDEs and the theory of global attractors. Cambridge Texts in Applied Mathematics: Cambridge University Press; 2001.
   Google Scholar
• Temam R. Infinite-dimensional dynamical systems in mechanics and physics. Philadelphia (PA): SIAM; 1995.
   Google Scholar
• Chueshov I. Dynamics of quasi-Stable dissipative systems. Berlin: Springer; 2015.
   Google Scholar
• Ma TF, Monteiro RN. Singular limit and long-time dynamics of bresse systems. SIAM J Math Anal. 2017;49:2468–2495.
   Web of Science ®Google Scholar