On increasing stability in an inverse source problem with local boundary data at many wave numbers

2020 ◽  
pp. 1-13
Author(s):  
Victor Isakov
Keyword(s):  
Boundary Data ◽  
Inverse Source Problem ◽  
Local Boundary ◽  
Wave Numbers

Lipschitz stability for a hyperbolic inverse problem by finite local boundary data

2006 ◽  
Vol 85 (10) ◽  
pp. 1219-1243 ◽  
Author(s):  
M. Bellassoued ◽  
D. Jellali ◽  
M. Yamamoto
Keyword(s):  
Inverse Problem ◽  
Boundary Data ◽  
Lipschitz Stability ◽  
Local Boundary

scholarly journals On the low frequency asymptotics for the 2-D electromagnetic transmission problem

2006 ◽  
Vol 47 (3) ◽  
pp. 397-411
Author(s):  
C. N. Anestopoulos ◽  
E. E. Argyropoulos
Keyword(s):  
Boundary Data ◽  
Maxwell Equations ◽  
Low Frequency ◽  
Boundary Integral ◽  
Transmission Problem ◽  
Integral Equation Methods ◽  
Wave Numbers ◽  
Homogeneous Media ◽  
Electromagnetic Transmission ◽  
Dimensional Domain

AbstractWe examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.

scholarly journals Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Yavar Kian ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Boundary Data ◽  
Stability Estimate ◽  
Carleman Estimate ◽  
Parabolic Problems ◽  
Conditional Stability ◽  
Inverse Source Problem ◽  
Lateral Boundary ◽  
Spatial Component

Abstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n ) {x=(x_{1},\ldots,x_{n})} and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component x n {x_{n}} by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.

Local boundary data of eigenfunctions on a Riemannian symmetric space

1989 ◽  
Vol 98 (3) ◽  
pp. 639-657 ◽  
Author(s):  
E. P. van den Ban ◽  
H. Schlichtkrull
Keyword(s):  
Symmetric Space ◽  
Boundary Data ◽  
Riemannian Symmetric Space ◽  
Local Boundary

Numerical Experimental for an Inverse Source Problem Method

2021 ◽  
pp. 125-139
Author(s):  
Abdalkaleg Atia Idris Hamad
Keyword(s):  
Boundary Data ◽  
Noise Intensity ◽  
Source Function ◽  
Elliptic Systems ◽  
Background Field ◽  
Inverse Source Problem ◽  
Performance Accuracy ◽  
Problem Method ◽  
Error Field ◽  
Well Posed

This paper examines extensions of an iterative method for inverse evaluation of the source function for two elliptic systems. The method begins with a starting value for the undetermined source. Next, a background field and equations for the error field are obtained. 2-D domains are considered. This method is suitable for Helmholtz and Poisson operators. In the presence of finite-difference grid resolution, a varying amount of boundary data, and methods of filtering the noise in the boundary data and the noise intensity of the boundary data, the performance, accuracy, and iteration count of the algorithm are investigated. Keywords: Source, Inverse Problems, Poisson, Noise, Ill-Posedness, Well-Posed

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