Hölder stability estimate of Robin coefficient in corrosion detection with a single boundary measurement

2015 ◽  
Vol 31 (11) ◽  
pp. 115009 ◽  
Author(s):  
Guanghui Hu ◽  
Masahiro Yamamoto
Keyword(s):  
Stability Estimate ◽  
Corrosion Detection ◽  
Boundary Measurement ◽  
Single Boundary ◽  
Hölder Stability

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.

scholarly journals Global stability for an inverse problem in soil–structure interaction

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150117 ◽  
Author(s):  
G. Alessandrini ◽  
A. Morassi ◽  
E. Rosset ◽  
S. Vessella
Keyword(s):  
Inverse Problem ◽  
Soil Structure ◽  
Stability Estimate ◽  
Unknown Coefficient ◽  
Thin Elastic Plate ◽  
Concentrated Force ◽  
Reaction Coefficient ◽  
Slab Foundation ◽  
Interior Points ◽  
Hölder Stability

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal deflection is measured at the interior points. We prove a global Hölder stability estimate under (mild) regularity assumptions on the unknown coefficient.

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