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Global attractor and stabilization for a coupled PDE-ODE system

Efendiev, M and Zelik, S (2011) Global attractor and stabilization for a coupled PDE-ODE system arXiv.

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Abstract

We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem. In the case where the ODE-component of the system is monotone, we establish the existence of a smooth global attractor of finite Hausdorff and fractal dimension. The case of the non-monotone ODE-component is much more complicated. In particular, the set of equilibria becomes non-compact here and contains a huge number of essentially discontinuous solutions. Nevertheless, we prove the stabilization of any trajectory to a single equilibrium if the coupling constant is small enough.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Efendiev, MUNSPECIFIEDUNSPECIFIED
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 9 October 2011
Related URLs :
Additional Information : This is an arXiv publication.
Depositing User : Symplectic Elements
Date Deposited : 07 Jan 2015 18:35
Last Modified : 07 Jan 2015 18:35
URI: http://epubs.surrey.ac.uk/id/eprint/806846

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