Author:
Bouzitouna Abdallah,Boussetila Nadjib,Rebbani Faouzia
Abstract
Abstract
This paper deals with the problem of determining an unknown boundary condition
u
(
0
)
in the boundary value problem
u
y
y
(
y
)
−
A
u
(
y
)
=
0
,
u
(
0
)
=
f
,
u
(
+
∞
)
=
0
, with the aid of an extra measurement at an internal point. It is well known that such a problem is severely ill-posed, i.e., the solution does not depend continuously on the data. In order to overcome the instability of the ill-posed problem, we propose two regularization procedures: the first method is based on the spectral truncation, and the second is a version of the Kozlov-Maz’ya iteration method. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution.
MSC: 35R25, 65J20, 35J25.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Cited by
13 articles.
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