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Entropy-energy inequalities and improved convergence rates for nonlinear parabolic equations
Robust exponential attractors for population dynamics models with infinite time delay
1. | Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini, 50, I-20133 Milano, Italy |
2. | Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, I-20133 Milano |
[1] |
Vittorino Pata. Exponential stability in linear viscoelasticity with almost flat memory kernels. Communications on Pure and Applied Analysis, 2010, 9 (3) : 721-730. doi: 10.3934/cpaa.2010.9.721 |
[2] |
Valeria Danese, Pelin G. Geredeli, Vittorino Pata. Exponential attractors for abstract equations with memory and applications to viscoelasticity. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 2881-2904. doi: 10.3934/dcds.2015.35.2881 |
[3] |
Peter E. Kloeden, José Real, Chunyou Sun. Robust exponential attractors for non-autonomous equations with memory. Communications on Pure and Applied Analysis, 2011, 10 (3) : 885-915. doi: 10.3934/cpaa.2011.10.885 |
[4] |
S. Gatti, M. Grasselli, V. Pata, M. Squassina. Robust exponential attractors for a family of nonconserved phase-field systems with memory. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 1019-1029. doi: 10.3934/dcds.2005.12.1019 |
[5] |
Hunseok Kang. Dynamics of local map of a discrete Brusselator model: eventually trapping regions and strange attractors. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 939-959. doi: 10.3934/dcds.2008.20.939 |
[6] |
Manil T. Mohan. Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with "fading memory". Evolution Equations and Control Theory, 2022, 11 (1) : 125-167. doi: 10.3934/eect.2020105 |
[7] |
A. Jiménez-Casas. Invariant regions and global existence for a phase field model. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 273-281. doi: 10.3934/dcdss.2008.1.273 |
[8] |
Corrado Mascia. Stability analysis for linear heat conduction with memory kernels described by Gamma functions. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3569-3584. doi: 10.3934/dcds.2015.35.3569 |
[9] |
José A. Langa, Alain Miranville, José Real. Pullback exponential attractors. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1329-1357. doi: 10.3934/dcds.2010.26.1329 |
[10] |
Jon Jacobsen, Taylor McAdam. A boundary value problem for integrodifference population models with cyclic kernels. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3191-3207. doi: 10.3934/dcdsb.2014.19.3191 |
[11] |
Jianhong Wu, Weiguang Yao, Huaiping Zhu. Immune system memory realization in a population model. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 241-259. doi: 10.3934/dcdsb.2007.8.241 |
[12] |
Andrea Caravaggio, Luca Gori, Mauro Sodini. Population dynamics and economic development. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5827-5848. doi: 10.3934/dcdsb.2021178 |
[13] |
Kei Matsuura, Mitsuharu Otani. Exponential attractors for a quasilinear parabolic equation. Conference Publications, 2007, 2007 (Special) : 713-720. doi: 10.3934/proc.2007.2007.713 |
[14] |
Hermano Frid. Invariant regions under Lax-Friedrichs scheme for multidimensional systems of conservation laws. Discrete and Continuous Dynamical Systems, 1995, 1 (4) : 585-593. doi: 10.3934/dcds.1995.1.585 |
[15] |
Sandra Carillo. Materials with memory: Free energies & solution exponential decay. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1235-1248. doi: 10.3934/cpaa.2010.9.1235 |
[16] |
Tomás Caraballo, José Real, I. D. Chueshov. Pullback attractors for stochastic heat equations in materials with memory. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 525-539. doi: 10.3934/dcdsb.2008.9.525 |
[17] |
Monica Conti, Elsa M. Marchini, V. Pata. Global attractors for nonlinear viscoelastic equations with memory. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1893-1913. doi: 10.3934/cpaa.2016021 |
[18] |
V. V. Chepyzhov, A. Miranville. Trajectory and global attractors of dissipative hyperbolic equations with memory. Communications on Pure and Applied Analysis, 2005, 4 (1) : 115-142. doi: 10.3934/cpaa.2005.4.115 |
[19] |
Jianbo Yuan, Shixuan Zhang, Yongqin Xie, Jiangwei Zhang. Attractors for a class of perturbed nonclassical diffusion equations with memory. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021261 |
[20] |
Paweł Góra, Abraham Boyarsky, Zhenyang LI, Harald Proppe. Statistical and deterministic dynamics of maps with memory. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4347-4378. doi: 10.3934/dcds.2017186 |
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