Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1146-1157.

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Lifespan Estimation of Solutions to Cauchy Problem of Semilinear Wave Equation

Jiang Hongbiao1, Wang Haihang2   

  1. 1 Department of Mathematics, Lishui University, Zhejiang Lishui 323000;
    2 School of Science, Zhejiang Sci-Tech University, Hangzhou 310018
  • Received:2018-09-27 Revised:2018-12-24 Published:2019-11-08
  • Supported by:
    Supported by the Natural Science Foundation of Zhejiang Province(LY18A010008)

Abstract: In this paper, the lifespan estimate to the Cauchy problem of the semi-linear wave equation utt utt-△u=(1+|x|2)α|u|p in Rn is studied. The upper bound of lifespan is improved for the cases n=2,1 < p ≤ 2 and n=1,p > 1, by using the improved Kato's type lemma.

Key words: Semilinear wave equations, Initial value problems, Ordinary differential inequality, Lifespan

CLC Number: 

  • O175