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 & Continuous Dynamical Systems - A, 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 & Continuous Dynamical Systems - B, 2006, 6 (5) : 1051-1076. doi: 10.3934/dcdsb.2006.6.1051
[2]

Valeria Danese, Pelin G. Geredeli, Vittorino Pata. Exponential attractors for abstract equations with memory and applications to viscoelasticity. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2881-2904. doi: 10.3934/dcds.2015.35.2881
[3]

Monica Conti, Elsa M. Marchini, V. Pata. Global attractors for nonlinear viscoelastic equations with memory. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1893-1913. doi: 10.3934/cpaa.2016021
[4]

V. V. Chepyzhov, A. Miranville. Trajectory and global attractors of dissipative hyperbolic equations with memory. Communications on Pure & Applied Analysis, 2005, 4 (1) : 115-142. doi: 10.3934/cpaa.2005.4.115
[5]

Michele Coti Zelati. Global and exponential attractors for the singularly perturbed extensible beam. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 1041-1060. doi: 10.3934/dcds.2009.25.1041
[6]

Peter E. Kloeden, José Real, Chunyou Sun. Robust exponential attractors for non-autonomous equations with memory. Communications on Pure & Applied Analysis, 2011, 10 (3) : 885-915. doi: 10.3934/cpaa.2011.10.885
[7]

S. Gatti, M. Grasselli, V. Pata, M. Squassina. Robust exponential attractors for a family of nonconserved phase-field systems with memory. Discrete & Continuous Dynamical Systems - A, 2005, 12 (5) : 1019-1029. doi: 10.3934/dcds.2005.12.1019
[8]

Hunseok Kang. Dynamics of local map of a discrete Brusselator model: eventually trapping regions and strange attractors. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 939-959. doi: 10.3934/dcds.2008.20.939
[9]

A. Jiménez-Casas. Invariant regions and global existence for a phase field model. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 273-281. doi: 10.3934/dcdss.2008.1.273
[10]

Alessia Berti, Valeria Berti, Ivana Bochicchio. Global and exponential attractors for a Ginzburg-Landau model of superfluidity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (2) : 247-271. doi: 10.3934/dcdss.2011.4.247
[11]

José A. Langa, Alain Miranville, José Real. Pullback exponential attractors. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1329-1357. doi: 10.3934/dcds.2010.26.1329
[12]

Vittorino Pata. Exponential stability in linear viscoelasticity with almost flat memory kernels. Communications on Pure & Applied Analysis, 2010, 9 (3) : 721-730. doi: 10.3934/cpaa.2010.9.721
[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]

Gianluca Mola. Global attractors for a three-dimensional conserved phase-field system with memory. Communications on Pure & Applied Analysis, 2008, 7 (2) : 317-353. doi: 10.3934/cpaa.2008.7.317
[15]

Monica Conti, Vittorino Pata. On the regularity of global attractors. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1209-1217. doi: 10.3934/dcds.2009.25.1209
[16]

Tomás Caraballo, José Real, I. D. Chueshov. Pullback attractors for stochastic heat equations in materials with memory. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 525-539. doi: 10.3934/dcdsb.2008.9.525
[17]

Etsushi Nakaguchi, Koichi Osaki. Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2627-2646. doi: 10.3934/dcdsb.2013.18.2627
[18]

Miguel Ângelo De Sousa Mendes. Quasi-invariant attractors of piecewise isometric systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 323-338. doi: 10.3934/dcds.2003.9.323
[19]

Leonardo Mora. Homoclinic bifurcations, fat attractors and invariant curves. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1133-1148. doi: 10.3934/dcds.2003.9.1133
[20]

Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 579-596. doi: 10.3934/dcds.2006.15.579

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences