Acta Mathematica Vietnamica

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On the Global Attractor for a Semilinear Strongly Degenerate Parabolic Equation
Mai Xuan Thao

 

Abstract

We prove the existence of a global attractor in S20(Ω)L2p2(Ω) for a semilinear strongly degenerate parabolic equation in a bounded domain with the homogeneous Dirichlet boundary condition, in which the nonlinearity satisfies a polynomial type condition of arbitrary order and the external force belongs to L 2(Ω). This global attractor is then shown to have a finite fractal dimension in L 2(Ω). We also study the existence and exponential stability of the unique stationary solution to the problem.

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