Missing boundary data reconstruction by the factorization method

被引：3

作者：

Ben Abda, Amel ^{[1
]}

Henry, Jacques ^{[2
]}

Jday, Fadhel ^{[1
]}

机构：

[1] LAMSIN ENIT, Tunis, Tunisia

[2] Univ Bordeaux 1, INRIA Bordeaux Sud Ouest, IMB, F-33405 Talence, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2009年 / 347卷 / 9-10期

关键词：

D O I：

10.1016/j.crma.2009.03.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the data completion problem for the Laplace equation in a cylindrical domain. The Neumann and Dirichlet boundary conditions are given on one face of the cylinder while there is no condition on the other face. This Cauchy problem has been known since Hadamard (1953) to be ill-posed. Here it is set as an optimal control problem with a regularized cost function. We use the factorization method for elliptic boundary value problems. For each set of Cauchy data, to obtain the estimate of the missing data one has to solve a parabolic Cauchy problem in the cylinder and a linear equation. The operator appearing in these problems satisfy a Riccati equation that does not depend on the data. To cite this article: A. Ben Abda et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：501 / 504

页数：4

共 6 条

[1]

AZAIEZ M, 2006, INVERSE PROBL, V21, P1915

[2]

Ben Abda A, 2005, INVERSE PROBL, V34, P81

[3] AN OPTIMAL-CONTROL PROBLEM FOR A PARABOLIC EQUATION IN NON-CYLINDRICAL DOMAINS [J].