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

Volume 61 / 2013

Cung The Anh, Le Thi Thuy 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.

Authors

  • Cung The AnhDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy, Cau Giay
    Hanoi, Vietnam
    e-mail
  • Le Thi ThuyDepartment of Mathematics
    Electric Power University
    235, Hoang Quoc Viet, Tu Liem
    Hanoi, Vietnam
    e-mail

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