论文标题
在分数弹性的反问题中的唯一性
Uniqueness in an inverse problem of fractional elasticity
论文作者
论文摘要
我们研究了分数弹性的反问题。与线性弹性的经典问题相比，我们考虑了与分数dirichlet到neumann数据相关的与线性的，各向同性分数弹性算子相关的LAMé参数的唯一恢复。在我们的分析中，我们通过概括了所谓的liouville降低，利用分数矩阵schrödinger方程，这是一种经典的标量电导率方程研究的技术。我们得出的结论是，如果Lamé参数同意并且在外部恒定，并且它们的泊松比在任何地方都一致，那么独特的恢复是可能的。我们的研究是由于非局部弹性领域的重大活性所激发的。
We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lamé parameters associated to a linear, isotropic fractional elasticity operator from fractional Dirichlet-to-Neumann data. In our analysis we make use of a fractional matrix Schrödinger equation via a generalization of the so-called Liouville reduction, a technique classically used in the study of the scalar conductivity equation. We conclude that unique recovery is possible if the Lamé parameters agree and are constant in the exterior, and their Poisson ratios agree everywhere. Our study is motivated by the significant recent activity in the field of nonlocal elasticity.
