Electron. J. Diff. Equ., Vol. 2012 (2012), No. 203, pp. 1-18.

Existence and upper semi-continuity of uniform attractors for non-autonomous reaction diffusion equations on R^N

Tang Quoc Bao

Abstract:
We prove the existence of uniform attractors for the non-autonomous reaction diffusion equation
$$ u_t - \Delta u + f(x,u) + \lambda u = g(t,x) $$
on $\mathbb{R}^N$, where the external force g is translation bounded and the nonlinearity f satisfies a polynomial growth condition. Also, we prove the upper semi-continuity of uniform attractors with respect to the nonlinearity.

Submitted April 10, 2012. Published November 24, 2012.
Math Subject Classifications: 34D45, 35B41, 35K57, 35B30.
Key Words: Uniform attractors; reaction diffusion equations; unbounded domain; upper semicontinuity.

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Tang Quoc Bao
School of Applied Mathematics and Informatics
Ha Noi University of Science and Technology
1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam
email: baotangquoc@gmail.com

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