Abstract
We consider the waves propagating in the Einstein-de Sitter spacetime, which obey the covariant d’Alembert’s equation. We construct the parametrixes in the terms of Fourier integral operators and discuss the propagation and reflection of the singularities phenomena.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Einstein, W. de Sitter, On the relation between the expansion and the mean density of the universe, in Proc. Natn. Acad. Sci. U.S.A, vol. 18 (1932), pp. 213–214
A. Galstian, T. Kinoshita, K. Yagdjian, A note on wave equation in Einstein & de Sitter spacetime. J. Math. Phys. 51, 052501 (2010)
L. Nirenberg, Lectures on Linear Partial Differential Equations (American. Math. Soc., Providence, 1973)
H. Ohanian, R. Ruffini, in Gravitation and Spacetime (Norton, New York, 1994)
K. Taniguchi, Y. Tozaki, A hyperbolic equation with double characteristics which has a solution with branching singularities. Math. Jpn. 25, 279–300 (1980)
K. Yagdjian, A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain. J. Differ. Equ. 206, 227–252 (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Galstian, A. (2015). Microlocal Analysis for Hyperbolic Equations in Einstein-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_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-12577-0_27
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-12576-3
Online ISBN: 978-3-319-12577-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)