Geodesic
Boussinesq -- Löve mathematical model on a geometrical graph
Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 82-97

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

Of concern is the Boussinesq – Löve mathematical model describing longitudinal vibrations in the elements of construction that can be represented in the form of a finite connected oriented graph. Differential equations on graphs is a relatively new piece of mathematical knowledge. The article deals with Sobolev type equations on graphs. The Fourier method is used for solution of the problem. The article besides introduction, conclusion and list of references contains four paragraphs. The first paragraph describes the properties of eigenvalues and eigenfunctions of the problem on a graph. The second section is devoted to specific examples of solutions of the Sturm – Liouville problem. In the third paragraph, by applying the Fourier method, the solutions of the Boussinesq – Löve problem are found. In the last paragraph, the possibility of usage of the Fourier method for Boussinesq – Löve problem for some finite connected oriented graphs is justified.
Keywords: Sobolev type model, geometrical graph, Fourier method, Sturm – Liouville problem. 
@article{JCEM_2015_2_2_a7,
     author = {A. A. Zamyshlyaeva and A. V. Lut},
     title = {Boussinesq -- {L\"ove} mathematical model on a geometrical graph},
     journal = {Journal of computational and engineering mathematics},
     pages = {82--97},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a7/}
}
TY  - JOUR
AU  - A. A. Zamyshlyaeva
AU  - A. V. Lut
TI  - Boussinesq -- Löve mathematical model on a geometrical graph
JO  - Journal of computational and engineering mathematics
PY  - 2015
SP  - 82
EP  - 97
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a7/
LA  - en
ID  - JCEM_2015_2_2_a7
ER  - 
%0 Journal Article
%A A. A. Zamyshlyaeva
%A A. V. Lut
%T Boussinesq -- Löve mathematical model on a geometrical graph
%J Journal of computational and engineering mathematics
%D 2015
%P 82-97
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a7/
%G en
%F JCEM_2015_2_2_a7
A. A. Zamyshlyaeva; A. V. Lut. Boussinesq -- Löve mathematical model on a geometrical graph. Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 82-97. http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a7/