Pullback Attractors for a Non-Autonomous Semilinear Degenerate Parabolic Equation on ℝ N

Abstract

In this paper, we prove the existence of pullback attractors for the following non-autonomous semilinear degenerate parabolic equation on ℝN: $$\frac{\partial u}{\partial t} - \textup{div} (\sigma (x)\nabla u) + \lambda u+ f(x,u) = g(x,t), $$ under a new condition concerning a variable non-negative diffusivity σ(⋅), an arbitrary polynomial growth order of the nonlinearity f and an exponent growth of the non-autonomous external force g.