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- Title
An inverse problem for an integro‐differential operator on a star‐shaped graph.
- Authors
Bondarenko, Natalia P.
- Abstract
A partial inverse problem for an integro‐differential Sturm‐Liouville operator on a star‐shaped graph is studied. We suppose that the convolution kernels are known on all the edges of the graph except one and recover the kernel on the remaining edge from a part of the spectrum. We prove the uniqueness theorem for this problem and develop a constructive algorithm for its solution, based on the reduction of the inverse problem on the graph to the inverse problem on the interval by using the Riesz basis property of the special system of functions.
- Subjects
INVERSE problems; NUMERICAL solutions to integro-differential equations; GRAPH theory; KERNEL functions; UNIQUENESS (Mathematics)
- Publication
Mathematical Methods in the Applied Sciences, 2018, Vol 41, Issue 4, p1697
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4698