Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Analysis of PDEs
2017-04-19 v3 Mathematical Physics
math.MP
Abstract
We are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Keywords
Cite
@article{arxiv.1610.06324,
title = {Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions},
author = {Yuriy Golovaty and Volodymyr Flyud},
journal= {arXiv preprint arXiv:1610.06324},
year = {2017}
}
Comments
18 pages, 3 figures