Pullback exponential attractors in nonlocal Mindlin's strain gradient porous elasticity

References

• Eringen AC. Linear theory of nonlocal elasticity and dispersion of plane waves. Int J Eng Sci. 1972;10:425–435. doi: 10.1016/0020-7225(72)90050-X
   Web of Science ®Google Scholar
• Mindlin R. Micro-structure in linear elasticity. Arch Ration Mech Anal. 1964;16:51–78. doi: 10.1007/BF00248490
   Web of Science ®Google Scholar
• Mindlin R. Second gradient of strain and surface-tension in linear elasticity. Int J Solids Struct. 1965;1:414–438. doi: 10.1016/0020-7683(65)90006-5
   Google Scholar
• Ieşan D. A gradient theory of porous elastic solids. Z Angew Math Mech. 2020;100:1–18. doi: 10.1002/zamm.201900241
   Web of Science ®Google Scholar
• Ieşan D. On the grade consistent theories of micromorphic solids. Am Inst Phys Conf Proc. 2011;1329:130–149. doi: 10.1063/1.3546081
   Google Scholar
• Liu Z, Magaña A, Quintanilla R. On the time decay of solutions for non-simple elasticity with voids. Z Angew Math Mech. 2016;96:857–873. doi: 10.1002/zamm.v96.7
   Web of Science ®Google Scholar
• Aouadi M, Passarella F, Tibullo V. Exponential stability in Mindlin's Form II gradient thermoelasticity with microtemperatures of type III. Proc R Soc. 2020;A 476:20200459. doi: 10.1098/rspa.2020.0459
   Google Scholar
• Aouadi M, Amendola A, Tibullo V. Asymptotic behavior in Form II Mindlin's strain gradient theory for porous thermoelastic diffusion materials. J Therm Stress. 2020;43:191–209. doi: 10.1080/01495739.2019.1653802
   Web of Science ®Google Scholar
• Aouadi M. Well-posedness, lack of analyticity and exponential stability in nonlocal Mindlin's strain gradient porous elasticity. Z Angew Math Phys. 2022;73:111. doi: 10.1007/s00033-022-01764-2
   Web of Science ®Google Scholar
• Aouadi M. Asymptotic behavior in nonlocal Mindlin's strain gradient thermoelasticity with voids and microtemperatures. J Math Anal Appl. 2022;514:126268. doi: 10.1016/j.jmaa.2022.126268
   Web of Science ®Google Scholar
• Singh D, Kaur G, Tomar SK. Waves in nonlocal elastic solid with voids. J Elast. 2017;128:85–114. doi: 10.1007/s10659-016-9618-x
   Web of Science ®Google Scholar
• Nunziato JW, Cowin SC. A nonlinear theory of elastic materials with voids. Arch Ration Mech Anal. 1979;72:175–201. doi: 10.1007/BF00249363
   Web of Science ®Google Scholar
• Munoz Rivera JE, Quintanilla R. On the time polynomial decay in elastic solids with voids. J Math Anal Appl. 2008;338:1296–1309. doi: 10.1016/j.jmaa.2007.06.005
   Web of Science ®Google Scholar
• Santos ML, Campelo ADS, Almeida Jùnior DS. On the decay rates of porous elastic systems. J Elast. 2017;127:79–101. doi: 10.1007/s10659-016-9597-y
   Web of Science ®Google Scholar
• Efendiev M, Zeli S, Miranville A. Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Proc R Soc Edinb Sect A. 2005;135:703–730. doi: 10.1017/S030821050000408X
   Google Scholar
• Czaja R, Marín-Rubio P. Pullback exponential attractors for parabolic equations with dynamical boundary conditions. Taiwan J Math. 2017;21:819–839. doi: 10.11650/tjm/7862
   Web of Science ®Google Scholar
• Hammami MA, Mchiri L, Netchaoui S, et al. Pullback exponential attractors for differential equations with variable delays. Discrete Contin Dyn Syst Ser B. 2020;25:301–319. doi: 10.3934/dcdss.2020367
   Web of Science ®Google Scholar
• Langa JA, Miranville A, Real J. Pullback exponential attractors. Discrete Contin Dyn Syst Ser B. 2010;26:1329–1357. doi: 10.3934/dcds.2010.26.1329
   Web of Science ®Google Scholar
• Li Y, Yang Z. Robustness of attractors for non-autonomous Kirchhoff wave models with strong nonlinear damping. Appl Math Optim. 2021;84:245–272. doi: 10.1007/s00245-019-09644-4
   Web of Science ®Google Scholar
• Ma TF, Monteiro RN, Pereira AC. Pullback dynamics of non-autonomous Timoshenko systems. Appl Math Optim. 2019;80:391–413. doi: 10.1007/s00245-017-9469-2
   Web of Science ®Google Scholar
• Yang Z, Li Y. Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous Kirchhoff wave models. Discrete Contin Dyn Syst Ser B. 2018;38:2629–2653. doi: 10.3934/dcds.2018111
   Web of Science ®Google Scholar
• You B. Pullback exponential attractors for some non-autonomous dissipative dynamical systems. Math Methods Appl Sci. 2021;44:10361–10386. doi: 10.1002/mma.v44.13
   Web of Science ®Google Scholar
• Aouadi M. Hölder continuity of exponential pullback attractors for Form II Mindlin's strain gradient viscoelastic plate. Discrete Contin Dyn Syst Ser B. 2023. doi: 10.3934/dcdsb.2023117
   Web of Science ®Google Scholar
• Carvalho AN, Sonner S. Pullback exponential attractors for evolution processes in Banach spaces: theoretical results. Commun Pure Appl Anal. 2013;12:3047–3071. doi: 10.3934/cpaa.2013.12.3047
   Web of Science ®Google Scholar
• Freitas MM. Pullback attractors for non-autonomous porous elastic system with nonlinear damping and sources terms. Math Methods Appl Sci. 2020;43:658–681. doi: 10.1002/mma.v43.2
   Web of Science ®Google Scholar
• Freitas MM, Costa AAC, Araújo GM. Pullback dynamics of a non-autonomous mixture problem in one dimensional solids with nonlinear damping. Commun Pure Appl Anal. 2020;19:785–809. doi: 10.3934/cpaa.2020037
   Web of Science ®Google Scholar
• Li YJ, Wang SY, Wu HQ. Pullback attractors for non-autonomous reaction-diffusion equations in Lp. Appl Math Comput. 2009;207:373–379. doi: 10.1016/j.cam.2008.05.007
   Web of Science ®Google Scholar
• Wang Y. On the upper semicontinuity of pullback attractors with applications to plate equations. Commun Pure Appl Anal. 2010;9:1653–1673. doi: 10.3934/cpaa.2010.9.1653
   Web of Science ®Google Scholar
• Wang YH, Zhong CK. Upper semicontinuity of pullback attractors for nonautonomous Kirchhoff wave models. Discrete Contin Dyn Syst Ser B. 2013;33:3189–3209. doi: 10.3934/dcds.2013.33.3189
   Web of Science ®Google Scholar
• Yang L, Yang MH, Kloeden PE. Pullback attractors for non-autonomous quasilinear parabolic equations with a dynamical boundary condition. Discrete Contin Dyn Syst Ser B. 2012;17:2635–2651. doi: 10.3934/dcdsb.2012.17.2635
   Web of Science ®Google Scholar
• Yang Z, Li L. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete Contin Dyn Syst Ser B. 2019;24:899–4912. doi: 10.3934/dcdsb.2019036
   Web of Science ®Google Scholar
• Yang XG, Nascimento Marcelo JD, Pelicer ML. Uniform attractors for non-autonomous plate equations with p-Laplacian perturbation and critical nonlinearities. Discrete Contin Dyn Syst Ser A. 2020;40:1937–1961. doi: 10.3934/dcds.2020100
   Web of Science ®Google Scholar
• Lions JL. Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod; 1969.
   Google Scholar
• Carvalho AN, Langa JA, Robinson JC. Attractors for infinite-dimensional non-autonomous dynamical systems. New York: Springer; 2013. p. 409. (Applied mathematical sciences; 182).
   Google Scholar
• Czaja R, Efendiev M. Pullback exponential attractors for nonautonomous equations part I: semilinear parabolic problems. J Math Anal Appl. 2011;381:748–765. doi: 10.1016/j.jmaa.2011.03.053
   Web of Science ®Google Scholar
• Carvalho AN, Sonner S. Pullback exponential attractors for evolution processes in Banach spaces: properties and applications. Commun Pure Appl Anal. 2014;13:1141–1165. doi: 10.3934/cpaa.2014.13.1141
   Web of Science ®Google Scholar