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2003 The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging
M. Efendiev, S. Zelik
Adv. Differential Equations 8(6): 673-732 (2003). DOI: 10.57262/ade/1355926831

Abstract

The longtime behaviour of solutions of a reaction-diffusion system with the nonlinearity rapidly oscillating in time ($f=f(t/{\varepsilon},u)$) is studied. It is proved that (under the natural assumptions) this behaviour can be described in terms of global (uniform) attractors $\mathcal A^{\varepsilon}$ of the corresponding dynamical process and that these attractors tend as ${\varepsilon}\to 0$ to the global attractor $\mathcal A^0$ of the averaged autonomous system. Moreover, we give a detailed description of the attractors $\mathcal A^{\varepsilon}$, ${\varepsilon}\ll1$, in the case where the averaged system possesses a global Liapunov function.

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M. Efendiev. S. Zelik. "The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging." Adv. Differential Equations 8 (6) 673 - 732, 2003. https://doi.org/10.57262/ade/1355926831

Information

Published: 2003
First available in Project Euclid: 19 December 2012

zbMATH: 1030.35016
MathSciNet: MR1969651
Digital Object Identifier: 10.57262/ade/1355926831

Subjects:
Primary: 35B41
Secondary: 35K57 , 37L30

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.8 • No. 6 • 2003
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