On Inverse Problems for the Wave Equation with Time Dependent Potentials

2019 ◽  
pp. 255-266
Author(s):  
G.F. Roach
Keyword(s):  
Wave Equation ◽  
Inverse Problems ◽  
Time Dependent

scholarly journals Counterexamples to inverse problems for the wave equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tony Liimatainen ◽  
Lauri Oksanen
Keyword(s):  
Wave Equation ◽  
Inverse Problems ◽  
Wave Operator ◽  
Time Dependent ◽  
Lorentzian Manifolds ◽  
Minkowski Metric ◽  
Lorentzian Metrics ◽  
Partial Data ◽  
Dirichlet To Neumann Map

<p style='text-indent:20px;'>We construct counterexamples to inverse problems for the wave operator on domains in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^{n+1} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ n \ge 2 $\end{document}</tex-math></inline-formula>, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are smooth and non-degenerate. On <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^{n+1} $\end{document}</tex-math></inline-formula> the metrics are conformal to the Minkowski metric.</p>

scholarly journals Uniqueness for time-dependent inverse problems with single dynamical data

2021 ◽  
Vol 497 (2) ◽  
pp. 124910
Author(s):  
Ibtissem Ben Aïcha ◽  
Guang-Hui Hu ◽  
Manmohan Vashisth ◽  
Jun Zou
Keyword(s):  
Inverse Problems ◽  
Time Dependent

An exact non reflecting boundary condition for 2D time-dependent wave equation problems

Wave Motion ◽  
2014 ◽  
Vol 51 (1) ◽  
pp. 168-192 ◽  
Author(s):  
Silvia Falletta ◽  
Giovanni Monegato
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Time Dependent

Stable recovery of the time-dependent source term from one measurement for the wave equation

2015 ◽  
Vol 31 (10) ◽  
pp. 105011 ◽  
Author(s):  
Kamal Rashedi ◽  
Mourad Sini
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Time Dependent
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