Inverse problem on a tree-shaped network: unified approach for uniqueness
Inverse problem on a tree-shaped network: unified approach for uniqueness
复制标题
树形网络上的逆问题：唯一性的统一方法
DOI：
10.1080/00036811.2014.985214
复制
发表时间：
2015
影响因子：
1.1
通讯作者：
M. Yamamoto
中科院分区：
文献类型：
--
作者：
L. Baudouin;M. Yamamoto
In this article, we prove uniqueness results for coefficient inverse problems regarding wave, heat or Schrödinger equation on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the wave equation. The objective is the determination of the potential on each edge of the network from the additional measurement of the solution at all but one external end points. Several results have already been obtained in this precise setting or in similar cases, and our main goal is to propose a unified and simpler method of proof of some of these results. The idea which we will develop for proving the uniqueness is to use a more traditional approach in coefficient inverse problems by Carleman estimates. Afterwards, using an observability estimate on the whole network, we apply a compactness–uniqueness argument and prove the stability for the wave inverse problem.
