scholarly journals Singular support of the scattering kernel for the wave equation perturbed in a bounded domain

1983 ◽  
Vol 59 (1) ◽  
pp. 13-16 ◽  
Author(s):  
Hideo Soga
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Singular Support ◽  
Scattering Kernel

Reflection of singularities of solutions to the wave equation and the leading singularity of the scattering kernel

1980 ◽  
Vol 86 (3-4) ◽  
pp. 235-242 ◽  
Author(s):  
H. D. Alber
Keyword(s):  
Wave Equation ◽  
Scattering Kernel

SynopsisIn this paper the reflection of singularities of solutions to the wave equation is studied using progressing wave expansions. The results are used to calculate the leading singularity of the Lax–Phillips scattering kernel, thus generalizing earlier results of Majda.

Uniqueness and non-uniqueness in acoustic tomography of moving fluid

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexey D. Agaltsov ◽  
Roman G. Novikov
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Harmonic Wave ◽  
Acoustic Tomography ◽  
Time Harmonic ◽  
Moving Fluid

AbstractWe consider a model time-harmonic wave equation of acoustic tomography of moving fluid in an open bounded domain in ℝ

scholarly journals The operatorB*Lfor the wave equation with Dirichlet control

2004 ◽  
Vol 2004 (7) ◽  
pp. 625-634 ◽  
Author(s):  
I. Lasiecka ◽  
R. Triggiani
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Arbitrary Dimension ◽  
Energy Methods ◽  
Smooth Bounded Domain ◽  
Dirichlet Boundary Control

In the case of the wave equation, defined on a sufficiently smooth bounded domain of arbitrary dimension, and subject to Dirichlet boundary control, the operatorB*Lfrom boundary to boundary is bounded in theL2-sense. The proof combines hyperbolic differential energy methods with a microlocal elliptic component.

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.

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