Asymptotic behavior of population dynamics models with nonlocal distributed delays

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Positive solutions of an integro-differential equation in all space with singular nonlinear term

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

Abstract
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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

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