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

Asymptotic behavior of population dynamics models with nonlocal distributed delays

  • 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:  December 31, 2006
Published:  September 2008
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35B41, 92D25; Secondary: 45K05.

    Citation:
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