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Energy Solutions for Nonlinear Klein–Gordon Equations in de Sitter Spacetime

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

The Cauchy problem for nonlinear Klein–Gordon equations is considered in de Sitter spacetime. The nonlinear terms are power type or exponential type. The local and global solutions are shown in the energy class.

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Acknowledgement

The author is thankful to Professors Karen Yagdjian, Michael Reissig, and Fumihiko Hirosawa for the invitation to the session “Qualitative properties of evolution models.” He is also thankful to the anonymous referee for the detailed comments on the paper.

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Authors and Affiliations

  1. Department of Mathematical sciences, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata, 990-8560, Japan

    Makoto Nakamura

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  1. Makoto Nakamura
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Correspondence to Makoto Nakamura .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Nakamura, M. (2015). Energy Solutions for Nonlinear Klein–Gordon Equations in de Sitter Spacetime. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_24

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