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arXiv · 1110.1837

Global attractor and stabilization for a coupled PDE-ODE system

Messoud Efendiev·Sergey Zelik
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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.

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Messoud Efendiev, Sergey Zelik. 2011-10-09. Global attractor and stabilization for a coupled PDE-ODE system. https://arxiv.org/abs/1110.1837

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