We consider a boundary identification problem arising in nondestructive testing of materials. The problem is to recover a part ΓI ⊂ ∂Ω of the boundary of a bounded, planar domain Ω from one Cauchy data pair (u, ∂u/∂ν) of a harmonic potential u in Ω collected on an accessible boundary subset ΓA ⊂ ∂Ω. We prove Fréchet differentiability of a suitably defined forward map, and discuss local uniqueness and Lipschitz stability results for the linearized problem.
Linearization of a free boundary problem in corrosion detection
CABIB, Elio;SINCICH, EVA
2011-01-01
Abstract
We consider a boundary identification problem arising in nondestructive testing of materials. The problem is to recover a part ΓI ⊂ ∂Ω of the boundary of a bounded, planar domain Ω from one Cauchy data pair (u, ∂u/∂ν) of a harmonic potential u in Ω collected on an accessible boundary subset ΓA ⊂ ∂Ω. We prove Fréchet differentiability of a suitably defined forward map, and discuss local uniqueness and Lipschitz stability results for the linearized problem.File in questo prodotto:
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