On inverse problems arising in fractional elasticity

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2021-09-08 DOI:10.4171/jst/428

Li Li

引用次数: 9

Abstract

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an inverse problem for a nonlinear fractional Lam\'e system. Our arguments are based on the unique continuation property for the fractional operator as well as the associated Runge approximation property.

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分数阶弹性的反问题

我们首先提出了一个线性分式Lam’e系统的反问题。我们从Dirichlet到Neumann映射的外部部分测量确定Lam’e参数。我们进一步研究了一个反障碍问题以及一个非线性分数阶Lam’e系统的反问题。我们的论点是基于分数算子的唯一连续性质以及相关的Runge近似性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.