Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 169-180.

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Blow-up of Solutions to the Euler-Poisson-Darboux-Tricomi Equation with a Nonlinear Memory Term

Baiping Ouyang()   

  1. Department of Apllied Mathematics, Guangzhou Huashang College, Guangzhou 511300
  • Received:2021-10-26 Revised:2022-08-25 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    Key Projects of Universities in Guangdong Province (NATURAL SCIENCE)(2019KZDXM042);Innovation Team Project in Colleges and Universities of Guangdong Province(2020WCXTD008);Science Foundation of Guangzhou Huashang College(2020HSDS01);Science Foundation of Guangzhou Huashang College(2021HSKT01)


Blow-up phenomenon of solutions to the Euler-Poisson-Darboux-Tricomi equation with a nonlinear memory term in the subcritical case is studied. By using functional methods associated with a modified Bessel equation, an iteration frame and the first lower bound are derived. Then, nonexistence of global solutions to the Cauchy problem for the Euler-Poisson-Darboux-Tricomi equation and an upper bound estimate of solutions for the lifespan are obtained via the iteration technique.

Key words: Nonlinear memory term, Euler-Poisson-Darboux-Tricomi equation, Blow-up

CLC Number: 

  • O175.2