GAUGE FREEDOMS IN THE ANISOTROPIC ELASTIC DIRICHLET-TO-NEUMANN MAP

被引：0

作者：

Ilmavirta, Joonas ^{[1
]}

Schluter, Hjordis ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla, Finland

来源：

INVERSE PROBLEMS AND IMAGING | 2024年

关键词：

Dirichlet-to-Neumann map; inverse problems; elastic wave equation; Riemannian geometry; anisotropic stiffness tensor; INVERSE PROBLEM; BOUNDARY CONTROL; DENSITY; UNIQUENESS;

D O I：

10.3934/ipi.2024055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We address the inverse problem of recovering the stiffness tensor and density of mass from the Dirichlet-to-Neumann map. We study the invariance of the Euclidean and Riemannian elastic wave equation under coordinate transformations. Furthermore, we present gauge freedoms between the parameters that leave the elastic wave equations invariant. We use these results to present gauge freedoms in the Dirichlet-to-Neumann map associated to the Riemannian elastic wave equation.

引用

页码：816 / 828

页数：13

共 20 条

[1] Recent progress in the boundary control method
Belishev, M. I.
[J]. INVERSE PROBLEMS, 2007, 23 (05) : R1 - R67
[2] The dynamical Lame system: Regularity of solutions, boundary controllability and boundary data continuation
Belishev, MI
Lasiecka, I
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2002, 8 : 143 - 167
[3] De Hoop MV, 2021, Arxiv, DOI arXiv:1901.03902
[4] UNIQUE RECOVERY OF PIECEWISE ANALYTIC DENSITY AND STIFFNESS TENSOR FROM THE ELASTIC-WAVE DIRICHLET-TO-NEUMANN MAP
De Hoop, Maarten, V
Nakamura, Gen
Zhai, Jian
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2019, 79 (06) : 2359 - 2384
[5] RECONSTRUCTION OF LAME MODULI AND DENSITY AT THE BOUNDARY ENABLING DIRECTIONAL ELASTIC WAVEFIELD DECOMPOSITION
De Hoop, Maarten V.
Nakamura, Gen
Zhai, Jian
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2017, 77 (02) : 520 - 536
[6] de Hoop Maarten V., 2021, PURE APPL ANAL, V3, P789, DOI DOI 10.2140/PAA.2021.3.789
[7] WELL-POSEDNESS OF SYSTEMS OF LINEAR ELASTICITY WITH DIRICHLET BOUNDARY CONTROL AND OBSERVATION
Guo, Bao-Zhu
Zhang, Zhi-Xiong
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (04) : 2139 - 2167
[8] The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds
Hintz, Peter
Uhlmann, Gunther
Zhai, Jian
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2022, 47 (12) : 2363 - 2400
[9] Katchalov A., 2001, Monographs and Surveys in Pure and Applied Mathematics, V123
[10] Kohn R.V., 1984, SIAM AMS P, P113, DOI [10.1002/cpa.3160370302, DOI 10.1002/CPA.3160370302]

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