Geodesic
Structure of mixed problem solution for wave equation on compact geometrical graph in nonzero initial velocity case
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 3, pp. 37-46 
O. V. Korovina; V. L. Pryadiev. Structure of mixed problem solution for wave equation on compact geometrical graph in nonzero initial velocity case. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 3, pp. 37-46. http://geodesic.mathdoc.fr/item/ISU_2009_9_3_a6/
@article{ISU_2009_9_3_a6,
     author = {O. V. Korovina and V. L. Pryadiev},
     title = {Structure of mixed problem solution for wave equation on compact geometrical graph in nonzero initial velocity case},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {37--46},
     year = {2009},
     volume = {9},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_3_a6/}
}
TY  - JOUR
AU  - O. V. Korovina
AU  - V. L. Pryadiev
TI  - Structure of mixed problem solution for wave equation on compact geometrical graph in nonzero initial velocity case
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2009
SP  - 37
EP  - 46
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ISU_2009_9_3_a6/
LA  - ru
ID  - ISU_2009_9_3_a6
ER  - 
%0 Journal Article
%A O. V. Korovina
%A V. L. Pryadiev
%T Structure of mixed problem solution for wave equation on compact geometrical graph in nonzero initial velocity case
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2009
%P 37-46
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/ISU_2009_9_3_a6/
%G ru
%F ISU_2009_9_3_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

A D'Alambert formula analogue for wave equation on the compact geometrical graph with generalized smooth transmission conditions is being proved.

[1] Yurko V. A., “O vosstanovlenii operatorov Shturma–Liuvillya na grafakh”, Mat. zametki, 79:4 (2006), 619–630 | DOI | MR | Zbl

[2] Pryadiev V. L., “Opisanie resheniya nachalno-kraevoi zadachi dlya volnovogo uravneniya na odnomernoi prostranstvennoi seti cherez funktsiyu Grina sootvetstvuyuschei kraevoi zadachi dlya obyknovennogo differentsialnogo uravneniya”, Sovremennaya matematika i ee prilozheniya, 38, Tbilisi, 2006, 82–94

[3] Pryadiev V. L., “Chislennaya skhema resheniya nachalno-kraevoi zadachi dlya volnovogo uravneniya na odnomernoi prostranstvennoi seti pri obobschenno-gladkikh usloviyakh transmissii”, Vestn. Samar. gos. un-ta. Estestvennonauch. ser., 8/2(67), 2008, 195–202

[4] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L. i dr., Differentsialnye uravneniya na geometricheskikh grafakh, FIZMATLIT, M., 2004, 272 pp. | Zbl

[5] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Izd-vo MGU, M., 1999, 799 pp. | MR

[6] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya: V 3 t., v. II, Gos. izd-vo fiz.-mat. lit., M., 1959, 808 pp.