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Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on

Tom 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

Streszczenie

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.

Autorzy

  • 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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