Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (1): 36-48.

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Asymptotic Behavior of the Solution for the Nonclassical Diffusion Equations with Fading Memory on the Whole Space R3

Ma Qiaozhen, Xu Ling, Zhang Yanjun   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070
  • Received:2015-04-01 Revised:2015-11-21 Online:2016-02-25 Published:2016-02-25
  • Supported by:

    Supported by the NSFC (11101334, 11361053), the NSF of Gansu Province (145RJZA112, 145RJZA232) and the Research Funds of Gansu Universities

Abstract:

We prove the existence of global attractors for the nonclassical diffusion equations with fading memory ututu-∫0k(su(t-s)ds+f(x, u)=g(x) defined on the entire space R3, where nonlinearity f(x, u) is critical.

Key words: Nonclassical diffusion equation, Fading memory, Critical nonlinearity, Unbounded domain, Global attractor

CLC Number: 

  • O175.8
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