Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on $\mathbb R^N$

Cung The Anh ¹   ; Le Thi Thuy ²

¹ Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
² Department of Mathematics Electric Power University 235, Hoang Quoc Viet, Tu Liem Hanoi, Vietnam

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 47-65

Résumé

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.

Détail

DOI : 10.4064/ba61-1-6

Keywords: prove existence global attractors following semilinear degenerate parabolic equation mathbb frac partial partial text div sigma nabla lambda under condition concerning variable nonnegative diffusivity sigma cdot arbitrary polynomial growth order nonlinearity overcome difficulties caused lack compactness embeddings these results proved combining tail estimates method asymptotic priori estimate method