Green operators for low regularity spacetimes
Green operators for low regularity spacetimes
In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well-posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs.
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Sanchez Sanchez, Yafet
72589503-da03-4d66-9429-f3598ce7681e
Vickers, James
719cd73f-c462-417d-a341-0b042db88634
Sanchez Sanchez, Yafet
72589503-da03-4d66-9429-f3598ce7681e
Vickers, James
719cd73f-c462-417d-a341-0b042db88634
Sanchez Sanchez, Yafet and Vickers, James
(2018)
Green operators for low regularity spacetimes.
Journal of Physics: Conference Series, 968 (1), .
(doi:10.1088/1742-6596/968/1/012011).
Abstract
In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well-posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs.
Text
Sanchez_Sanchez_2018_J._Phys.__Conf._Ser._968_012011
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Accepted/In Press date: 6 January 2018
e-pub ahead of print date: 22 February 2018
Identifiers
Local EPrints ID: 418718
URI: https://eprints.soton.ac.uk/id/eprint/418718
ISSN: 1742-6588
PURE UUID: 6fc6dbd7-64a2-4913-aa53-70f994ad9286
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Date deposited: 20 Mar 2018 17:30
Last modified: 20 Jul 2019 01:28
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Author:
Yafet Sanchez Sanchez
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