Advertisement

Semilinear Hyperbolic Equations in Curved Spacetime

  • Karen YagdjianEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

This is a survey of the author’s recent work rather than a broad survey of the literature. The survey is concerned with the global in time solutions of the Cauchy problem for matter waves propagating in the curved spacetimes, which can be, in particular, modeled by cosmological models. We examine the global in time solutions of some class of semililear hyperbolic equations, such as the Klein–Gordon equation, which includes the Higgs boson equation in the Minkowski spacetime, de Sitter spacetime, and Einstein & de Sitter spacetime. The crucial tool for the obtaining those results is a new approach suggested by the author based on the integral transform with the kernel containing the hypergeometric function.

Keywords

de Sitter spacetime Klein–Gordon equation global solutions Huygens’ principle Higuchi bound 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas-Pan AmericanEdinburgUSA

Personalised recommendations