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September  2006, 6(5): 1051-1076. doi: 10.3934/dcdsb.2006.6.1051

Robust exponential attractors for population dynamics models with infinite time delay

Cecilia Cavaterra 1, and  M. Grasselli 2,

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

Received  November 2005 Revised  January 2006 Published  June 2006

We consider an integrodifferential reaction-diffusion system which finds application in population dynamics. The memory kernels accounting for delay effects can be of both weak and strong type. Rescaling the kernels with a time relaxation $\varepsilon>0$, we show that the original model gives raise to a one-parameter family of dynamical systems in a suitable phase-space, We prove that this family is characterized by a corresponding family of exponential attractors which is stable as the delay effects vanish, i.e., when $\varepsilon$ goes to $0$.
Keywords: Population dynamics, invariant regions, memory kernels, exponential attractors..
Mathematics Subject Classification: Primary: 35B41, 92D25; Secondary: 37L25, 45K0.
Citation: 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
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