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Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime

Author

Listed:
  • Kimitoshi Tsutaya

    (Hirosaki University)

  • Yuta Wakasugi

    (Hiroshima University)

Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. The blow-up condition is the same as in the accelerated expanding Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We also show the same results for the space derivative nonlinear term.

Suggested Citation

  • Kimitoshi Tsutaya & Yuta Wakasugi, 2022. "Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime," Partial Differential Equations and Applications, Springer, vol. 3(1), pages 1-10, February.
    • Handle: RePEc:spr:pardea:v:3:y:2022:i:1:d:10.1007_s42985-021-00145-0
    DOI: 10.1007/s42985-021-00145-0
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