Inverse source problem for a system of wave equations on a Lorentzian manifold

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2 Citations (Scopus)

Abstract

A system of wave equations on a Lorentzian manifold, the coefficients of which depend on time relates to the Einstein equation in general relativity. We consider inverse source problem for the system in this paper. Having established the Carleman estimate with a second large parameter for the Laplace–Beltrami operator on a Lorentzian manifold under assumptions independent of a choice of local coordinates on a suitable weight function, we consider its application to the inverse source problem for the system and prove local Hölder stability.

Original languageEnglish
Pages (from-to)1414-1434
Number of pages21
JournalCommunications in Partial Differential Equations
Volume45
Issue number10
DOIs
Publication statusPublished - Oct 2 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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