JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 64-75.doi: 10.6040/j.issn.1671-9352.0.2019.459

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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

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

CLC Number: 

  • O175.29
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