V Pivovarchik, H. Woracek:

"Eigenvalue Asymptotics for a Star-Graph Damped Vibrations Problem";

in: "ASC Report 20/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

We consider a boundary value problem generated by Sturm-Liouville

equations on the edges of a star-shaped graph. Thereby a continuity condition

and a condition depending on the spectral parameter is imposed at

the interior vertex, corresponding to the case of damping in the problem

of small transversal vibrations of a star graph of smooth inhomogeneous

strings. At the pendant vertices Dirichlet boundary conditions are imposed.

We describe the eigenvalue asymptotics of the problem under

consideration.

Eigenvalue asymptotics, Sturm-Liouville theory, star-graph, Kirchhoff

http://www.asc.tuwien.ac.at/preprint/2010/asc20x2010.pdf

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