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The Maximum Principle and Sign-Changing Solutions of the Klein–Gordon Equation with the Higgs Potential in the de Sitter Spacetime

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Analysis, Probability, Applications, and Computation

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

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Abstract

In this chapter, we discuss the maximum principle for the linear equation and the sign-changing solutions of the semilinear equation with the Higgs potential. Numerical simulations indicate that the bubbles for the semilinear Klein–Gordon equation in the de Sitter spacetime are created and apparently exist for all times.

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Acknowledgements

The authors acknowledge the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing high-performance computing and visualization resources that have contributed to the research results reported within this paper. URL: http://www.tacc.utexas.edu. We also gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla K40 GPU used for this research. K.Y. was supported by the University of Texas Rio Grande Valley College of Sciences 2016–17 Research Enhancement Seed Grant.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, University of Texas RGV, Edinburg, TX, USA

    Karen Yagdjian & Andras Balogh

Authors
  1. Karen Yagdjian
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  2. Andras Balogh
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Corresponding author

Correspondence to Karen Yagdjian .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Karl‐Olof Lindahl

  2. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Torsten Lindström

  3. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

  5. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Patrik Wahlberg

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Yagdjian, K., Balogh, A. (2019). The Maximum Principle and Sign-Changing Solutions of the Klein–Gordon Equation with the Higgs Potential in the de Sitter Spacetime. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_36

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