American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Positive solutions of an integro-differential equation in all space with singular nonlinear term
  • DCDS Home
  • This Issue
  • Next Article
    Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping
December  2008, 22(4): 861-883. doi: 10.3934/dcds.2008.22.861

Asymptotic behavior of population dynamics models with nonlocal distributed delays

Cecilia Cavaterra 1, and  Maurizio Grasselli 2,

1. 

Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini, 50, I-20133 Milano
2. 

Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano

Received  January 2007 Published  September 2008

We consider an integrodifferential reaction-diffusion system on a multidimensional spatial domain, subject to homogeneous Neumann boundary conditions. This system finds applications in population dynamics and it is characterized by nonlocal delay terms depending on both the temporal and the spatial variables. The distributed time delay effects are represented by memory kernels which decay exponentially but they are not necessarily monotonically decreasing. We first show how to construct a (dissipative) dynamical system on a suitable phase-space. Then we discuss the existence of the global attractor as well as of an exponential attractor.
Keywords: Population dynamics, exponential attractors, invariant regions, global attractors, memory kernels, nonlocal effects.
Mathematics Subject Classification: Primary: 35B41, 92D25; Secondary: 45K05.
Citation: Cecilia Cavaterra, Maurizio Grasselli. Asymptotic behavior of population dynamics models with nonlocal distributed delays. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 861-883. doi: 10.3934/dcds.2008.22.861
[1]

Cecilia Cavaterra, M. Grasselli. Robust exponential attractors for population dynamics models with infinite time delay. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1051-1076. doi: 10.3934/dcdsb.2006.6.1051
[2]

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
[3]

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
[4]

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
[5]

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
[6]

Michele Coti Zelati. Global and exponential attractors for the singularly perturbed extensible beam. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 1041-1060. doi: 10.3934/dcds.2009.25.1041
[7]

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
[8]

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
[9]

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
[10]

Lin Yang, Yejuan Wang, Peter E. Kloeden. Exponential attractors for two-dimensional nonlocal diffusion lattice systems with delay. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1811-1831. doi: 10.3934/cpaa.2022048
[11]

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
[12]

Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206
[13]

Alessia Berti, Valeria Berti, Ivana Bochicchio. Global and exponential attractors for a Ginzburg-Landau model of superfluidity. Discrete and Continuous Dynamical Systems - S, 2011, 4 (2) : 247-271. doi: 10.3934/dcdss.2011.4.247
[14]

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
[15]

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
[16]

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
[17]

Lin Yang, Yejuan Wang, Tomás Caraballo. Regularity of global attractors and exponential attractors for $ 2 $D quasi-geostrophic equations with fractional dissipation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1345-1377. doi: 10.3934/dcdsb.2021093
[18]

Monica Conti, Vittorino Pata. On the regularity of global attractors. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1209-1217. doi: 10.3934/dcds.2009.25.1209
[19]

Gianluca Mola. Global attractors for a three-dimensional conserved phase-field system with memory. Communications on Pure and Applied Analysis, 2008, 7 (2) : 317-353. doi: 10.3934/cpaa.2008.7.317
[20]

Mirelson M. Freitas, Anderson J. A. Ramos, Manoel J. Dos Santos, Eraldo R. N. Fonseca. Attractors and pullback dynamics for non-autonomous piezoelectric system with magnetic and thermal effects. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3745-3765. doi: 10.3934/cpaa.2021129

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (70)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy