Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1816-1829.

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Existence and Blow-Up of a Parabolic Equation with Logarithmic Nonlinearity

Yuge Du(),Shuying Tian*()   

  1. School of Science, Wuhan University of Technology, Wuhan 430070
  • Received:2020-07-08 Online:2021-12-26 Published:2021-12-02
  • Contact: Shuying Tian;
  • Supported by:
    the NSFC(11601402);the Fundamental Research Funds for the Central Universities(2020IA003)


In this paper, we consider the initial boundary value problem of a viscoelastic equation with logarithmic nonlinearity. Under some suitable conditions, we obtain the existence of global weak solutions. Otherwise, we get that the solution does not blow up in any finite time. This is different from the situation of the viscoelastic equation with a polynomial nonlinearity, in which case the solution blows up in finite time.

Key words: Logarithmic nonlinearity, Viscoelastic term, Global existence, Blow-up

CLC Number: 

  • O175