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Upper Semicontinuity of Attractors and Synchronization

✍ Scribed by Alexandre N Carvalho; Hildebrando M Rodrigues; Tomasz Dłotko

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
282 KB
Volume
220
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we prove that diffusively coupled abstract semilinear parabolic systems synchronize. We apply the abstract results obtained 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.

📜 SIMILAR VOLUMES

Perturbation of the diffusion and upper
Perturbation of the diffusion and upper semicontinuity of attractors
✍ J.M. Arrieta; A.N. Carvalho; A. Rodríguez-Bernal 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 335 KB

We obtain uniform bounds for attractors of parabolic problems with nonlinear boundary conditions with respect to perturbations in the diffusion coefficients. These bounds are the main tool to obtain continuity properties of the attractors relatively to perturbations of the diffusion coefficient. We