The Wave Equation in a Bounded Domain

2018 ◽  
pp. 23-26
Author(s):  
Alain Haraux
Keyword(s):  
Wave Equation ◽  
Bounded Domain

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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