Inverse problems for the differential operator on a graph with cycles

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• 作者：Chuan-Fu Yang ^{chuanfuyang@mail.njust.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quantum graph ; Inverse spectral problem ; Inverse nodal problem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1548-1562
• 全文大小：371 K

文摘

This work deals with inverse problems of the Sturm–Liouville operator on a graph with multi-cycles, endowed with standard matching conditions in the internal vertex and with Neumann boundary conditions at the boundary vertices. We show that the potential on a graph with multi-cycles (including the potential on cycles) can be constructed by the dense nodal points on the interval considered. Moreover, we investigate the so-called incomplete inverse problems of recovering the potential on a fixed edge from a subset of nodal points situated only on a part of the edge.