The determination of a discontinuity in a conductivity from a single boundary measurement

1998 ◽  
Vol 14 (1) ◽  
pp. 67-82 ◽  
Author(s):  
Frank Hettlich ◽  
William Rundell
Keyword(s):  
Boundary Measurement ◽  
Single Boundary

Stable determination of corrosion by a single electrostatic boundary measurement

2003 ◽  
Vol 19 (4) ◽  
pp. 973-984 ◽  
Author(s):  
G Alessandrini ◽  
L Del Piero ◽  
L Rondi
Keyword(s):  
Boundary Measurement

Recovery of the heat equation from a single boundary measurement

2017 ◽  
Vol 97 (10) ◽  
pp. 1667-1676
Author(s):  
Amin Boumenir ◽  
Vu Kim Tuan
Keyword(s):  
Heat Equation ◽  
Boundary Measurement ◽  
Single Boundary

STABLE DETERMINATION OF A BOUNDARY COEFFICIENT IN AN ELLIPTIC EQUATION

2008 ◽  
Vol 18 (01) ◽  
pp. 107-123 ◽  
Author(s):  
JIN CHENG ◽  
MOURAD CHOULLI ◽  
JUNSHAN LIN
Keyword(s):  
Inverse Problem ◽  
Cauchy Problem ◽  
Boundary Function ◽  
Stability Estimate ◽  
Detection Problem ◽  
Corrosion Detection ◽  
Order Elliptic Operator ◽  
Logarithmic Stability ◽  
Single Boundary

We prove a logarithmic stability estimate for a Cauchy problem associated with a second order elliptic operator. Our proof is essentially based on a Carleman estimate by A. L. Bukhgeim. This result is applied to establish a stability estimate for the inverse problem of determining a boundary coefficient (or a boundary function) by a single boundary measurement. This kind of inverse problems is motivated by the corrosion detection problem.

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