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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

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 $0$.
Citation: 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
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