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Nesting inertial manifolds for reaction and diffusion equations with large diffusivity

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Rodríguez Bernal, Aníbal and Willie, Robert (2007) Nesting inertial manifolds for reaction and diffusion equations with large diffusivity. Nonlinear Analysis: Theory, Methods & Applications, 67 (1). pp. 70-93. ISSN 0362-546X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X06003233


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Abstract

We study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations. A priori, we review both local and global dynamics of the system in scales of Banach spaces of Hilbert type and we prove the existence of a universal compact attractor for the equations. Extensions yield the existence of a family of nesting inertial manifolds dependent on the diffusion of the system of equations. It is introduced an upper semicontinuity notion in large diffusivity for inertial manifolds. The limit inertial manifold whose dimension is strictly less than those of the infinite dimensional system of semilinear evolution equations is obtained.


Item Type:Article
Uncontrolled Keywords:Semilinear system of reaction-diffusion equations; Well posedness; Universal compact attractor; Inertial manifolds; Limit inertial manifold; Large diffusivity
Subjects:Sciences > Mathematics > Functions
ID Code:17693
Deposited On:16 Jan 2013 10:23
Last Modified:12 Dec 2018 15:07

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