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- W1620201775 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." @default.
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- W1620201775 date "2011-10-09" @default.
- W1620201775 modified "2023-10-18" @default.
- W1620201775 title "Global attractor and stabilization for a coupled PDE-ODE system" @default.
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