Counterexamples to inverse problems for the wave equation
| Autor: | Tony Liimatainen, Lauri Oksanen |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics, Inverse Problems |
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Differential Geometry
Inverse problems Control and Optimization Lorentzian manifold Conformal map partial data 35R30 35L05 58J45 01 natural sciences Combinatorics General Relativity and Quantum Cosmology Mathematics - Analysis of PDEs Minkowski space 111 Mathematics FOS: Mathematics ANISOTROPIC CALDERON PROBLEM Discrete Mathematics and Combinatorics Pharmacology (medical) 0101 mathematics NONUNIQUENESS counterexamples conformal scaling Physics Operator (physics) 010102 general mathematics Inverse problem Wave equation 010101 applied mathematics hidden conformal invariance UNIQUENESS Differential Geometry (math.DG) Modeling and Simulation MANIFOLDS wave equation Mathematics::Differential Geometry Analysis Analysis of PDEs (math.AP) Counterexample |
| Zdroj: | Inverse Problems & Imaging. 16:467 |
| ISSN: | 1930-8345 1930-8337 |
| DOI: | 10.3934/ipi.2021058 |
| Popis: | We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are smooth and non-degenerate. On $\mathbb{R}^{n+1}$ the metrics are conformal to the Minkowski metric. Comment: 12 |
| Databáze: | OpenAIRE |
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