Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1033-1041.

Previous Articles     Next Articles

Lifespan Estimate of Damped Semilinear Wave Equation in Exterior Domain with Neumann Boundary Condition

Jinglei Zhao1(),Jiacheng Lan1,*(),Shanshan Yang2()   

  1. 1 College of Teacher Education, Lishui University, Zhejiang Lishui 323000
    2 School of Science, Zhejiang Sci-Tech University, Hangzhou 310018
  • Received:2020-05-07 Online:2021-08-26 Published:2021-08-09
  • Contact: Jiacheng Lan;;


This paper concerns about the upper bound of lifespan estimate to damped semilinear wave equations in exterior domain with vanishing Neumann boundary condition. We find that the initial boundary value problem with Neumann boundary condition admits the same upper bound of lifespan as that of the Cauchy problem in $\mathbb{R}^n (n\ge 1)$. This fact is different from the zero Dirichlet boundary value problem in 2-D exterior domain for lifespan estimate, compared to the corresponding result in [6], and is also different from the zero Dirichlet boundary value problem on half line for critical power, compared to the result in [16].

Key words: Lifespan, Damped semilinear wave equations, Neumann boundary condition, Exterior problem

CLC Number: 

  • O175.2