Nesting inertial manifolds for reaction and diffusion equations with large diffusivity |
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Authors: | A Rodríguez Bernal Robert Willie |
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Institution: | 1. University of Madrid, Complutense, Applied Mathematics, 28040 Madrid, Spain;2. University of Zimbabwe, Department of Mathematics, Harare, Zimbabwe;3. University of KwaZulu-Natal, South Africa |
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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. |
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Keywords: | 35Bxx 35D40 35B45 35K57 |
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