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Pullback Attractors for a Non-Autonomous Semilinear Degenerate Parabolic Equation on $\mathbb R^N$
Nguyen Dinh Binh
,
Nguyen Nhu Thang
,
Le Thi Thuy
Abstract
In this paper, we prove the existence of pullback attractors for the following non-autonomous semilinear degenerate parabolic equation on $\mathbb R^N$: $$\frac{\partial u}{\partial t} - \textup{div} (\sigma (x)\nabla u) + \lambda u+ f(x,u) = g(x,t),$$ under a new condition concerning a variable non-negative diffusivity $\sigma(\cdot)$, an arbitrary polynomial growth order of the nonlinearity $f$ and an exponent growth of the non-autonomous external force $g$.