Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (4): 641-650.

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Exponential Attractors for Reaction-Diffusion Equations in H2(Ω) and L2P-2(Ω)

Wang Gang1, Tang Yanbin2   

  1. 1 School of Sciences, Hubei University of Technology, Wuhan 430068;
    2 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074
  • Received:2014-02-28 Revised:2015-03-17 Online:2015-08-25 Published:2015-08-25

Abstract:

A class of reaction-diffusion equations with arbitrary polynomial growth nonlinearity f and nonhomogeneous term g are concerned in this paper. We first construct exponential attractors in H2(Ω) for the underlying semigroup when Ω is a bounded open set in R3. We obtain this result by proving the Lipschitz continuity between some positively invariant absorbing set in L2(Ω) and some positively invariant absorbing set in H2(Ω). Then, we obtain exponential attractors in L2P-2(Ω) for any gL2(Ω) by using a new approaching technique. This improves the result in previous references.

Key words: Exponential attractors, Reaction-diffusion equations, Lipschitz continuity

CLC Number: 

  • O175.2
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