Asymptotics and scattering for wave Klein-Gordon systems

We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified version of global existence based on LeFloch-Ma, and then derive...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 48; no. 9; pp. 1102 - 1147
Main Authors Chen, Xuantao, Lindblad, Hans
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.09.2023
Taylor & Francis Ltd
Subjects
Asymptotic properties
Asymptotics
Infinity
Inverse problems
Klein-Gordon equation
Scattering
Scattering from infinity
Wave equations
Wave-Klein-Gordon systems
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ISSN0360-5302
1532-4133
DOI10.1080/03605302.2023.2263205

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Summary:We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified version of global existence based on LeFloch-Ma, and then derive the asymptotic behavior of the system. The asymptotics of the Klein-Gordon field consist of a modified phase times a homogeneous function, and the asymptotics of the wave equation consist of a radiation field in the wave zone and an interior homogeneous solution coupled to the Klein-Gordon asymptotics. We then consider the inverse problem, the scattering from infinity. We show that given the type of asymptotic behavior at infinity, there exist solutions of the system that present the exact same behavior.
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ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2023.2263205