Solution of Inverse Problems for Wave Equation with a Nonlinear Coefficient

2021 ◽  
Vol 61 (9) ◽  
pp. 1511-1520
Author(s):  
A. V. Baev
Keyword(s):  
Wave Equation ◽  
Inverse Problems ◽  
Nonlinear Coefficient

scholarly journals Some geometric inverse problems for the linear wave equation

2015 ◽  
Vol 9 (2) ◽  
pp. 371-393 ◽  
Author(s):  
Anna Doubova ◽  
◽  
Enrique Fernández-Cara
Keyword(s):  
Wave Equation ◽  
Inverse Problems ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Geometric Inverse Problems

On the uniqueness of inverse problems for the reduced wave equation with unknown embedded obstacles

2021 ◽  
Author(s):  
Jiaqing Yang ◽  
Meng Ding ◽  
Keji Liu
Keyword(s):  
Wave Equation ◽  
Inverse Problems ◽  
Bounded Domain ◽  
Open Subset ◽  
Wave Equations ◽  
A Priori ◽  
Singularity Analysis ◽  
Piecewise Constant ◽  
Small Domain ◽  
Dirichlet To Neumann Map

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.

Time Reversal as a Computational Tool in Acoustics and Elastodynamics

2014 ◽  
Vol 22 (03) ◽  
pp. 1430001 ◽  
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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