Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on $\mathbb R^N$
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 47-65
MSC: 35B41, 35K65, 35D05.
DOI: 10.4064/ba61-1-6
Abstract
We prove the existence of global attractors for the following semilinear degenerate parabolic equation on $\mathbb R^N$: $$ \frac{\partial u}{\partial t} - \text{div}(\sigma (x)\nabla u) + \lambda u+ f(x,u) = g(x),$$ under a new condition concerning the variable nonnegative diffusivity $\sigma(\cdot)$ and for an arbitrary polynomial growth order of the nonlinearity $f$. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.
