Upper semicontinuity of attractors and synchronization. (English) Zbl 0907.34039

Summary: The authors prove that diffusively coupled abstract semilinear parabolic systems synchronize. The abstract results obtained are applied to a class of ordinary differential equations and to reaction diffusion problems. The technique consists of proving that the attractors for the coupled differential equations are upper semicontinuous with respect to the attractor of a limiting problem, explicitly exhibited, in the diagonal.


34D45 Attractors of solutions to ordinary differential equations
35K57 Reaction-diffusion equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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