Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 203, pp. 1-18.
Title: Existence and upper semi-continuity of uniform attractors for
non-autonomous reaction diffusion equations on R^N
Author: Tang Quoc Bao (Ha Noi Univ. of Science and Tech., Hanoi, Vietnam)
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.