Geodesic
Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 125-138 
V. A. Yurko. Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 125-138. http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a2/
@article{MMO_2014_75_2_a2,
     author = {V. A. Yurko},
     title = {Inverse {Problem} for {Differential} {Operators} on {Spatial} {Networks} with {Different} {Orders} on {Different} {Edges}},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {125--138},
     year = {2014},
     volume = {75},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a2/}
}
TY  - JOUR
AU  - V. A. Yurko
TI  - Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2014
SP  - 125
EP  - 138
VL  - 75
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a2/
LA  - ru
ID  - MMO_2014_75_2_a2
ER  - 
%0 Journal Article
%A V. A. Yurko
%T Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2014
%P 125-138
%V 75
%N 2
%U http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a2/
%G ru
%F MMO_2014_75_2_a2

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study the inverse problem of recovering differential operators from spectra on compact star-type graphs when differential equations have different orders on different edges. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

[1] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L., Borovskikh A. V. i dr., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004 | Zbl

[2] Pokornyi Yu. V., Beloglazova T. V., Dikareva E. V., Perlovskaya T. V., “O funktsii Grina dlya lokalno vzaimodeistvuyuschei sistemy obyknovennykh uravnenii razlichnogo poryadka”, Matem. zametki, 74:1 (2003), 146–149 | DOI | MR

[3] Belishev M. I., “Boundary spectral inverse problem on a class of graphs (trees) by the BC method”, Inverse Problems, 20 (2004), 647–672 | DOI | MR | Zbl

[4] Yurko V. A., “Inverse spectral problems for Sturm–Liouville operators on graphs”, Inverse Problems, 21:3 (2005), 1075–1086 | DOI | MR | Zbl

[5] Yurko V. A., “Inverse problems for Sturm–Liouville operators on bush-type graphs”, Inverse Problems, 25:10 (2009), 105008 | DOI | MR | Zbl

[6] Yurko V. A., “Inverse spectral problems for differential operators on arbitrary compact graphs”, Journal of Inverse and Ill-Posed Problems, 18:3 (2010), 245–261 | DOI | MR | Zbl

[7] Yurko V. A., “An inverse problem for higher-order differential operators on star-type graphs”, Inverse Problems, 23:3 (2007), 893–903 | DOI | MR | Zbl

[8] Marchenko V. A., Operatory Shturma-Liuvilya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR

[9] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[10] Yurko V. A., Method of spectral mappings in the inverse problem theory, Inverse and Ill-Posed Problems Series, 31, VSP, Utrecht, 2002 | MR

[11] Yurko V. A., Vvedenie v teoriyu obratnykh spektralnykh zadach, Fizmatlit, M., 2007 | Zbl

[12] Yurko V. A., “Vosstanovlenie differentsialnykh operatorov na zvezdoobraznom grafe s raznymi poryadkami na raznykh rebrakh”, Izv. Sarat. un-ta (novaya seriya). Ser. Matematika. Mekhanika. Informatika, 13:1(2) (2013), 112–116 | Zbl