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Attractors for a class of perturbed nonclassical diffusion equations with memory

  • * Corresponding author: Yongqin Xie

    * Corresponding author: Yongqin Xie 

The work was partly supported by NSFS grants 51578080, 11101053, 71471020, Postgraduate scientific research innovation project of Hunan Province (CX20210751)

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  • In this paper, using a new operator decomposition method (or framework), we establish the existence, regularity and upper semi-continuity of global attractors for a perturbed nonclassical diffusion equation with fading memory. It is worth noting that we get the same conclusion in [7,14] as the perturbed parameters $ \nu = 0 $, but the nonlinearity $ f $ satisfies arbitrary polynomial growth condition rather than critical exponential growth condition.


    Correction: “College of Arts and Sciences” has been changed to "College of Science"; “Postgraduate scientific research innovation project of Hunan Province (CX20210751)” has been added to Fund Project. We apologize for any inconvenience this may cause.

    Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35K57.


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