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

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.