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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (6): 64-75.doi: 10.6040/j.issn.1671-9352.0.2019.459

• • 上一篇    

de Sitter时空中波动方程初值问题解的爆破

孟希望,王娟   

  1. 安徽师范大学数学与统计学院, 安徽 芜湖 241002
  • 发布日期:2020-06-01
  • 作者简介:孟希望(1995— ),男,硕士研究生,研究方向为偏微分方程. E-mail:3572861950@qq.com
  • 基金资助:
    安徽省自然科学基金资助项目(1408085MA01)

Blow up of solutions to wave equations in the de Sitter spacetime

MENG Xi-wang, WANG Juan   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China
  • Published:2020-06-01

摘要: 通过考虑一类特殊Klein-Gordon方程的Cauchy问题解来探究de Sitter时空中Klein-Gordon方程解的生命估计。用未知函数变换和运用热核的方法,以及半群的性质可以证明该Cauchy问题解的爆破,并求出解生命跨度的上界。

关键词: de Sitter时空, 波动方程, 爆破, 生命估计

Abstract: This paper mainly studies the lifespan of a solution to Klein-Gordon wave equations in the de Sitter spacetime by considering a special form of the Klein-Gordon equation and studying its Cauchy problem. By a transformation of unknowns and by using the method of heat kernel, as well as the properties of semigroup, the blow up of this Cauchy problem is proved, and the upper bound of its life span is also obtained.

Key words: de Sitter spacetime, wave equation, blow up, lifespan

中图分类号: 

  • O175.29
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