RECOVERY OF TRANSVERSAL METRIC TENSOR IN THE SCHRO spacing diaeresis DINGER EQUATION FROM THE DIRICHLET-TO-NEUMANN MAP

被引：0

作者：

Bellassoued, Mourad ^{[1
]}

Rezig, Zouhour ^{[2
]}

机构：

[1] Univ Tunis El Manar, Natl Engn Sch Tunis, ENIT LAMSIN, BP 37, Tunis 1002, Tunisia

[2] Univ Tunis El Manar, Fac Sci Tunis, ENIT LAMSIN, BP 37, Tunis 1002, Tunisia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2022年 / 15卷 / 05期

关键词：

  Inverse problem; Riemannian manifold; stability estimate; Dirichlet-to-Neumann map; geodesical ray transform; BOUNDARY-VALUE PROBLEM; STABILITY ESTIMATE; INVERSE PROBLEM; WAVE-EQUATION; RECONSTRUCTION; RIGIDITY;

D O I：

10.3934/dcdss.2021158

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the inverse problem of determining simple metrics on a compact Riemannian manifold from boundary measurements. We take this information in the dynamical Dirichlet-to-Neumann map associated to the Schrodinger equation. We prove in dimension n > 2 that the knowledge of the Dirichlet-to-Neumann map for the Schrodinger equation uniquely determines the simple metric (up to an admissible set). We also prove a Holder-type stability estimate by the construction of geometrical optics solutions of the Schrodinger equation and the direct use of the invertibility of the geodesical X-ray transform.

引用

页码：1061 / 1084

页数：24

共 29 条

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