scholarly journals UNIQUENESS FOR AN INVERSE PROBLEM FOR A DISSIPATIVE WAVE EQUATION WITH TIME DEPENDENT COEFFICIENT

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Mourad Bellassoued ◽  
Ibtissem Ben Aicha
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Time Dependent ◽  
Dirichlet To Neumann Map ◽  
Dissipative Wave Equation

This paper deals with an hyperbolic inverse problem of determining a time-dependent coefficient a appearing in a dissipative wave equation, from boundary observations. We prove in dimension n greater than two, that a can be uniquely determined in a precise subset of the domain, from the knowledge of the Dirichlet-to-Neumann map.

scholarly journals Inverse Problem: Stability for the aligned magnetic field by the Dirichlet-to-Neumann map for the wave equation in a periodic quantum waveguide

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Mejri Youssef
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Wave Equation ◽  
Stability Estimate ◽  
Quantum Waveguide ◽  
Magnetic Wave ◽  
Problem Stability ◽  
Problème Inverse ◽  
Dirichlet To Neumann Map ◽  
Aligned Magnetic Field

International audience Dans ce papier, on a prouvé une estimation de stabilité pour le problème inverse de dé-termination du champ magnétique dans l'équation des ondes donné sur un domaine non borné à partir de l'opérateur de Dirichlet-to-Neumann. On a montré un résultat de stabilité pour ce problème inverse, dont la démonstration est basée sur la construction de solutions optique géométrique pour l'équation des ondes avec un potentiel magnétique 1-périodique. ABSTRACT. We consider the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic wave equation in a periodic quantum cylindrical waveguide from boundary observations. The observation is given by the Dirichlet to Neumann map associated to the wave equation. We prove by means of the geometrical optics solutions of the magnetic wave equation that the knowledge of the Dirichlet-to-Neumann map determines uniquely the aligned magnetic field induced by a time independent and 1-periodic magnetic potential. We establish a Hölder-type stability estimate in the inverse problem.

Lp-estimates for the wave equation with time-dependent dissipation

2005 ◽  
Vol 135 (2) ◽  
pp. 393-412
Author(s):  
Tokio Matsuyama
Keyword(s):  
Wave Equation ◽  
Exterior Domain ◽  
Wave Speed ◽  
Energy Decay ◽  
Time Dependent ◽  
Local Energy ◽  
Lp Estimates ◽  
Dissipative Wave Equation ◽  
Scattering Rates

We are interested in Lp-estimates and scattering rates for the dissipative wave equation with time-dependent coefficients in an exterior domain outside a star-shaped obstacle. We want to notice the case that the support of dissipation expands strictly less than the wave speed. We develop a new cut-off method, which is time dependent. For this, we shall obtain the local energy decay over the time-dependent subdomain

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>

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