# Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

Yuriy Golovaty; Volodymyr Flyud

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 404-419
- ISSN: 2391-5455

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topYuriy Golovaty, and Volodymyr Flyud. "Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions." Open Mathematics 15.1 (2017): 404-419. <http://eudml.org/doc/288066>.

@article{YuriyGolovaty2017,

abstract = {We are interested in the 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.},

author = {Yuriy Golovaty, Volodymyr Flyud},

journal = {Open Mathematics},

keywords = {Metric graph; Hyperbolic equation; Singular perturbed problem; Asymptotics; Boundary layer; metric graph; hyperbolic equation; singular perturbed problem; asymptotics; boundary layer},

language = {eng},

number = {1},

pages = {404-419},

title = {Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions},

url = {http://eudml.org/doc/288066},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Yuriy Golovaty

AU - Volodymyr Flyud

TI - Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 404

EP - 419

AB - We are interested in the 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.

LA - eng

KW - Metric graph; Hyperbolic equation; Singular perturbed problem; Asymptotics; Boundary layer; metric graph; hyperbolic equation; singular perturbed problem; asymptotics; boundary layer

UR - http://eudml.org/doc/288066

ER -

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