BOUSSINESQ-L"OVE MATHEMATICAL MODEL ON A GEOMETRICAL GRAPH

A. A. Zamyshlyaeva, A. V. Lut

Abstract


Of concern is the Boussinesq - L"ove 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 - L"ove problem are found. In the last paragraph, the possibility of usage of the Fourier method for Boussinesq - L"ove problem for some finite connected oriented graphs is justified.

Keywords


Sobolev type model, geometrical graph, Fourier method, Sturm - Liouville problem.

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References


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