An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds

2020/05/21 by Peter Hintz, Günther Uhlmann, Hintz, Peter +4 · 5 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Boundary (topology) #Boundary value problem #Dirichlet distribution #FOS: Mathematics #Geometry #Inverse #Inverse problem #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Neumann boundary condition #Numerical methods in inverse problems #Physics #Plane wave #Quantum mechanics #Thermoelastic and Magnetoelastic Phenomena #Uniqueness #Wave equation #math.AP

paper · pdf · doi:10.48550/arxiv.2005.10447

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2020/05/21 · openalex created_date 2020/05/29 · arxiv created 2021/01/26 · arxiv updated 2021/01/27 · openalex updated_date 2026/08/05

Abstract

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the knowledge of the Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams can be used to derive uniqueness.

Citations

• Determination of vacuum space-times from the Einstein-Maxwell equations
• Inverse problems for real principal type operators

Cited by

• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography
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• Inverse problem for connections in semi-linear wave equations on Lorentzian manifolds
• X-ray imaging from nonlinear waves: numerical reconstruction of a cubic nonlinearity
• Riemannian and Lorentzian Calderón problem under Magnetic Perturbation
• The DC Kerr Effect in Nonlinear Optics

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