On some geometric inverse problems for nonscalar elliptic systems

被引：0

作者：

Araujo, Raul K. C. ^{[1
]}

Fernandez-Cara, Enrique ^{[2
]}

Souza, Diego A. ^{[1
]}

机构：

[1] Univ Fed Pernambuco, Dept Math, UFPE, BR-50740545 Recife, PE, Brazil

[2] Univ Seville, Dept EDAN, Aptdo 1160, Seville 41080, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 11期

关键词：

Inverse problems; Nonscalar elliptic systems; Unique continuation; Domain variation techniques; Reconstruction; IDENTIFICATION;

D O I：

10.1016/j.jde.2020.06.040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some particular situations, this provides a strategy that could be used to compute approximations to the solution of the inverse problem. In the proofs, we use techniques related to (local) Carleman estimates and differentiation with respect to the domain. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：9123 / 9143

页数：21

共 50 条

[1] On some inverse problems for elliptic equations and systems
Pyatkov S.G.
Journal of Applied and Industrial Mathematics, 2011, 5 (03) : 417 - 430
[2] SOME GEOMETRIC ASPECTS IN INVERSE PROBLEMS
Romanov, V. G.
EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, 2015, 3 (04): : 68 - 84
[3] Uniqueness for some semilinear elliptic inverse problems
2001, VSP BV (09):
[4] Numerical Solution to Some Inverse Problems for Elliptic Systems Using Pseudoinverse Matrices
Sergienko, I. V.
Deineka, V. S.
JOURNAL OF AUTOMATION AND INFORMATION SCIENCES, 2011, 43 (07) : 3 - 28
[5] On Some Degenerate Elliptic Equations Arising in Geometric Problems
Capuzzo Dolcetta I.
Leoni F.
Vitolo A.
Journal of Mathematical Sciences, 2018, 233 (4) : 446 - 461
[6] The numerical solution of same elliptic nonscalar problems with nonlinear discontinuities
Echevarria, R
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (03) : 131 - 147
[7] On some classes of inverse problems for parabolic and elliptic equations
Pyatkov, S. G.
Tsybikov, B. N.
JOURNAL OF EVOLUTION EQUATIONS, 2011, 11 (01) : 155 - 186
[8] Some inverse problems for elliptic matrices with zero diagonal
Fiedler, M
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 332 : 197 - 204
[9] On some classes of inverse problems for parabolic and elliptic equations
S. G. Pyatkov
B. N. Tsybikov
Journal of Evolution Equations, 2011, 11 : 155 - 186
[10] SOME GEOMETRIC INVERSE PROBLEMS FOR THE LINEAR WAVE EQUATION
Doubova, Anna
Fernandez-Cara, Enrique
INVERSE PROBLEMS AND IMAGING, 2015, 9 (02) : 371 - 393

← 1 2 3 4 5 →