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Stability and asymptotic behaviour of solutions for some partial functional differential equations
by
Khalil Ezzinbi
Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, BP . 2390, Marrakesh, Morocco
The aim of this work is to investigate the asymptotic behavior of solutions near hyperbolic stationary solutions for partial functional differential equations with infinite delay. We suppose that the linear part satisfies the Hille-Yosida condition on a Banach space and it is not necessarily densely defined. Firstly, we establish a new variation of constants formula for the
nonhomogeneous linear equations. Secondly, we use this formula and the
spectral decomposition of the phase space to show the existence of stable and unstable manifolds. The estimations of solutions on these manifolds are obtained. For illustration, we propose to study the stability of stationary solutions for the Lotka-Voltera model with diffusion.
Date received: January 16, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-78.