Inverse problems for quadratic derivative nonlinear wave equations

For semilinear wave equations on Lorentzian manifolds with quadratic derivative nonlinear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from the source-to-solution map, one can determine the Lorentzian m...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 44; no. 11; pp. 1140 - 1158
Main Authors Wang, Yiran, Zhou, Ting
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.11.2019
Taylor & Francis Ltd
Subjects
Inverse problems
Isomorphism
Lorentzian metric
Manifolds (mathematics)
Mathematical analysis
Nonlinear equations
nonlinear interaction of singularities
nonlinear wave equations
quadratic derivatives nonlinearity
Wave equations
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Summary:For semilinear wave equations on Lorentzian manifolds with quadratic derivative nonlinear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from the source-to-solution map, one can determine the Lorentzian metric up to diffeomorphisms.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2019.1612908