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Semilinear Wave Equation in the de Sitter Spacetime with Hyperbolic Spatial Part

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New Trends in Analysis and Interdisciplinary Applications

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

Abstract

For the Cauchy problem for the semilinear wave equation in the de Sitter spacetime the global in time existence of the solutions is still an open problem. In this paper we give estimates for the lifespan of the solutions of semilinear wave equation in the de Sitter spacetime with flat and hyperbolic spatial parts under some conditions on the order of the nonlinearity. In the case of hyperbolic spatial part the order of nonlinearity is less than the critical value given by Strauss conjecture.

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Authors and Affiliations

  1. School of Mathematical and Statistical Science, University of Texas RGV, 1201 W. University Dr., Edinburg, TX, 78539, USA

    Anahit Galstian

Authors
  1. Anahit Galstian
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Correspondence to Anahit Galstian .

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Editors and Affiliations

  1. Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macao

    Pei Dang

  2. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Min Ku

  3. Faculty of Science and Technology, Department of Mathematics, University of Macau, Taipa, Macao

    Tao Qian

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

    Luigi G. Rodino

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Galstian, A. (2017). Semilinear Wave Equation in the de Sitter Spacetime with Hyperbolic Spatial Part. In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_62

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