Stable determination of corrosion by a single electrostatic boundary measurement

Abstract

We prove an optimal stability estimate for an inverse Robin boundary value problem arising in corrosion detection by electrostatic boundary measurements.

Numerical modeling of iron corrosion due to an acidic aqueous solution

“…physical time). Interesting, but necessarily a posteriori, descriptions have been developed based on inverse modeling, quantitative description of the corroded area is elaborated on the bases of electrostatic measurements in situ (for example [6,1]). …”

Error analysis of a parameter expansion method for corrosion detection in a pipe

“…Moreover, assume that each point of Γ d lies on the boundary of a circle contained in Ω. Then for any two functions w (1) and w (2) satisfying the conditions:…”

Smoothness dependent stability in corrosion detection

“…Indeed under such additional a priori hypothesis, we derive a surface doubling inequality of this sort for sufficiently small radius r (see Subsection 4.2). 4) which allows us to deduce that the vanishing rate of u at the boundary is at most polynomial, that is 5) for sufficiently small radius r (see Subsection 4.2). Again by gathering a logarithmic stability estimate for the Cauchy problem and the above vanishing rate we provide a global stability estimate for γ with a single log.…”

“…The present inverse problem has been studied in [4] and in [11] in a two dimensional setting where the authors provided a global logarithmic stability estimate for the corrosion coefficient for C 1,α corroded boundary. Similar inverse problems have been studied for the heat equation [9] and for the Stokes equations [10], where logarithmic stability estimates for the Robin coefficient γ have been provided.…”