Linearization of a free boundary problem in corrosion detection

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:378

Article

Cabib, Elio²  Fasino, Dario¹  Sincich, Eva³ 

[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy

[2] Univ Udine, Dipartimento Ingn Civile, I-33100 Udine, Italy

[3] Univ Trieste, Dipartimento Matemat & Informat, Trieste, Italy

关键词: Corrosion detection;    Frechet differentiability;    Free boundary problem;    Robin boundary condition;    Stability;   

DOI  :  10.1016/j.jmaa.2011.02.011

来源: Elsevier

【 摘 要 】

We consider a boundary identification problem arising in nondestructive testing of materials. The problem is to recover a part Gamma(1) subset of partial derivative Omega of the boundary of a bounded, planar domain Omega from one Cauchy data pair (u, partial derivative u/partial derivative v) of a harmonic potential u in Omega collected on an accessible boundary subset Gamma(A) subset of partial derivative Omega. We prove Frechet differentiability of a suitably defined forward map, and discuss local uniqueness and Lipschitz stability results for the linearized problem. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free