A formulation for higher dimensional inverse problems for the wave equation

Abstract In this paper, we consider inverse problems associated with the reduced wave equation on a bounded domain Ω belongs to R^N (N >= 2) for the case where unknown obstacles are embedded in the domain Ω. We show that, if both the leading and 0-order coeﬃcients in the equation are a priori known to be piecewise constant functions, then both the coeﬃcients and embedded obstacles can be simultaneously recovered in terms of the local Dirichlet-to-Neumann map deﬁned on an arbitrary small open subset of the boundary \partial Ω. The method depends on a well-deﬁned coupled PDE-system constructed for the reduced wave equations in a suﬃciently small domain and the singularity analysis of solutions near the interface for the model.

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Dynamic Inverse Problems for the Acoustic Wave Equation

Time-dependent Problems in Imaging and Parameter Identification ◽

10.1007/978-3-030-57784-1_2 ◽

2020 ◽

pp. 25-49

Author(s):

Thies Gerken

Keyword(s):

Wave Equation ◽

Inverse Problems ◽

Acoustic Wave ◽

Acoustic Wave Equation ◽

Dynamic Inverse

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Inverse problems involving the one-way wave equation: medium function reconstruction

Mathematics and Computers in Simulation ◽

10.1016/s0378-4754(99)00100-7 ◽

1999 ◽

Vol 50 (5-6) ◽

pp. 489-510 ◽

Cited By ~ 2

Author(s):

David J.N. Wall ◽

Jonas Lundstedt

Keyword(s):

Wave Equation ◽

Inverse Problems ◽

The One ◽

Function Reconstruction

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Time Reversal as a Computational Tool in Acoustics and Elastodynamics

Journal of Computational Acoustics ◽

10.1142/s0218396x14300011 ◽

2014 ◽

Vol 22 (03) ◽

pp. 1430001 ◽

Cited By ~ 17

Author(s):

Dan Givoli

Keyword(s):

Wave Equation ◽

Simple Model ◽

Inverse Problems ◽

Time Reversal ◽

Review Paper ◽

Scalar Wave ◽

Computational Tool ◽

Personal View ◽

Scalar Wave Equation ◽

The Subject

In this review paper, the use of the Time Reversal (TR) method as a computational tool for solving some classes of inverse problems is surveyed. The basics of computational TR are explained, using the scalar wave equation as a simple model. The application of TR to various problems in acoustics and elastodynamics is reviewed, in a selective and biased way as it leans on the author's personal view, referring to representative articles published on the subject.

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