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Green operators for low regularity spacetimes

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.

1742-6588
1-14
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), 1-14. (doi:10.1088/1742-6596/968/1/012011).

Record type: Article

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.

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Accepted/In Press date: 6 January 2018
e-pub ahead of print date: 22 February 2018
Published date: 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
ORCID for James Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 20 Mar 2018 17:30
Last modified: 17 Oct 2019 00:40

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