Abstract
We consider a thin metallic plate whose top side is inaccessible
and in contact with a corroding fluid.
Heat exchange between metal and fluid follows
linear Newton's cooling law as long as the inaccessible side is not damaged.
We assume that the effects of corrosion are modeled by means
of a nonlinear perturbation in the exchange law. On the other hand,
we are able to heat the conductor and take temperature maps of the
accessible side.
Our goal is to recover the nonlinear perturbation
of the exchange law on the top side from thermal data collected
on the opposite one (thermal imaging). In this paper we use a stationary
model, i.e.,
the temperature inside the plate is assumed
to fulfill Laplace's equation.
Hence, our problem is stated as an inverse ill-posed problem
for Laplace's equation with nonlinear boundary conditions.
We study identifiability and local Lipschitz stability. In particular,
we prove that the nonlinear term is identified by one Cauchy data set.
Moreover,
we produce approximated solutions by means of an
optimizational method.
Anno
2006
Autori IAC
Tipo pubblicazione
Altri Autori
Fasino D., Inglese G.
Editore
Academic Press.
Rivista
IMA journal of applied mathematics