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.
Linearization of a free boundary problem in corrosion detection
CABIB, Elio;FASINO, Dario;
2011-01-01
Abstract
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.File in questo prodotto:
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