The Linearization of the Dirichlet-to-Neumann Map in the Anisotropic Kirchhoff-Love Plate Theory
The Linearization of the Dirichlet-to-Neumann Map in the Anisotropic Kirchhoff-Love Plate Theory
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各向异性Kirchhoff-Love板理论中Dirichlet-Neumann映射的线性化
DOI：
10.1137/s0036139994270437
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Masaru Ikehata
中科院分区：
文献类型：
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作者：
Masaru Ikehata
对于二维有界域上的每个 ${\bf C}$ 弹性张量场，我们可以自然地定义狄利克雷到诺依曼图，用 $\Pi _{\bf C} $ 表示，它是电阻抗断层扫描中电压到电流图的模拟（例如，参见调查论文 [The Dirichlet-to-Neumann map and applications, Inverse Problems in PDE, Society for Industrial and Applied Mathematics, Society for Industrial and Applied Mathematics, 1990]及其参考文献）。目前尚不清楚$\Pi _{\bf C} $是否唯一决定${\bf C}$。本文感兴趣的是映射${\bf C} \mapsto \Pi _{\bf C} $在齐次${\bf C}$处的Frechet导数，记为$d\Pi _{\bf C} $，并研究$\ker d\Pi _{\bf C}的“大小” $。主要结果如下： (1) 若$\ker d\Pi _{\bf C} = 0$，则${\bf C}$的所有Stroh特征值集合的个数必须为4。 (2) 如果 ${\bf C}$ 的所有 Stroh 特征值集合的计数为 4，并且 ${\bf C}$ 满足其分量 ${\bf ...
For each ${\bf C}$ elasticity tensor field over a two-dimensional bounded domain, we can naturally define the Dirichlet-to-Neumann map, denoted by $\Pi _{\bf C} $, which is an analogue of the voltage-to-current map in electrical impedance tomography (see for instance the survey paper [The Dirichlet-to-Neumann map and applications, Inverse Problems in PDE, Society for Industrial and Applied Mathematics, 1990] and the references therein). It is not known whether $\Pi _{\bf C} $ uniquely determines ${\bf C}$.In this paper, we are interested in the Frechet derivative of the map ${\bf C} \mapsto \Pi _{\bf C} $ at homogeneous ${\bf C}$, denoted by $d\Pi _{\bf C} $, and study the “size” of $\ker d\Pi _{\bf C} $. The main results are as follows: (1) If $\ker d\Pi _{\bf C} = 0$, the counting number of the set of all Stroh eigenvalues of ${\bf C}$ must be four. (2) If the counting number of the set of all Stroh eigenvalues of ${\bf C}$ is four and ${\bf C}$ satisfies an additional condition on its components ${\bf ...