Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Yurko V. A. On an inverse problem for differential operators on hedgehog-type graphs. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 1, pp. 65-72. DOI: 10.18500/1816-9791-2014-14-1-65-72, EDN: SCSSSF

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.03.2014
Full text:
(downloads: 192)
Language: 
Russian
Heading: 
UDC: 
517.984
EDN: 
SCSSSF

On an inverse problem for differential operators on hedgehog-type graphs

Autors: 
Yurko Vjacheslav Anatol'evich, Saratov State University
Abstract: 

An inverse spectral problem is studied for Sturm–Liouville differential operators on hedgehog-type graphs with generalized matching conditions in the interior vertices and with Dirichlet boundary conditions in the boundary vertices. A uniqueness theorem of recovering potentials from given spectral characteristics is provided, and a constructive solution for the inverse problem is obtained. 

References: 
  1.  Pokornyj Ju. V., Penkin O. M., Prjadiev V. L., Borovskih A. V., Lazarev K. P., Shabrov S. A. Differencial’nye uravnenija na geometricheskih grafah [Differential equations on the geometric graphs]. Moscow, Fizmatlit, 2004 (in Russian).
  2.  Langese J. E., Leugering G., Schmidt J. P. G. Modelling, analysis and control of dynamic elastic multi-link structures. Boston, Birkh ¨ auser, 1994. DOI : 10.1007/978-1-4612-0273-8.
  3.  Belishev M. I. Boundary spectral inverse problem on a class of graphs (trees) by the BC method. Inverse Problems, 2004, vol. 20, pp. 647–672. DOI: 10.1088/0266-5611/20/3/002.
  4. Yurko V. A. Inverse spectral problems for Sturm– Liouville operators on graphs. Inverse Problems, 2005, vol. 21, pp. 1075–1086. DOI : 10.1088/0266-5611/21/3/017.
  5. Yurko V. A. Inverse problems for Sturm–Liouville operators on graphs with a cycle. Operators and Matrices, 2008, vol. 2, no. 4, pp. 543–553. DOI: 10.7153/oam-02-34.
  6. Yurko V. A. Inverse problem for Sturm– Liouville operators on hedgehog-type graphs. Math. Notes, 2011, vol. 89, no. 3, pp. 438–449. DOI : 10.1134/S000143461103014X.
  7. Yurko V. A. Inverse problems for Sturm–Liouville operators on bush-type graphs. Inverse Problems, 2009. vol. 25, no. 10, 105008, 14 p. DOI: 10.1088/0266-5611/25/10/105008.
  8. Yurko V. A. Vvedenie v teoriju obratnyh spektral’nyh zadach [Introduction to the inverse spectral problems theory]. Moscow, Fizmatlit, 2007 (in Russian).
  9. Yurko V. A. Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-posed Problems Series. Utrecht, VSP, 2002.
  10. Yurko V. A. Quasi-periodic boundary value problems with discontinuity conditions inside the interval. Schriftenreiche des Fachbereichs Mathematik, SM–DU– 767, Universit ¨ at Duisburg–Essen, 2013, pp. 1–7.
  11. Yurko V. A. Integral transforms connected with discontinuous boundary value problems. Integral Transforms and Special Functions, 2000, vol. 10, no. 2, pp. 141–164. DOI : 10.1080/10652460008819282.
Received: 
03.09.2013
Accepted: 
08.01.2014
Published: 
28.02.2014