Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

• Autorzy: Yuriy Golovaty , Volodymyr Flyud
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Metric graph; Hyperbolic equation; Singular perturbed problem; Asymptotics; Boundary layer

Kategorie tematyczne

• 35R02: Partial differential equations on graphs and networks (ramified or polygonal spaces)
• 35L20: Initial-boundary value problems for second-order hyperbolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 404-419

Daty

wydano

2017-01-01

otrzymano

2016-10-21

zaakceptowano

2017-02-22

online

2017-04-09

Twórcy

autor

Yuriy Golovaty

• Ivan Franko National University of Lviv, Lviv,

autor

Volodymyr Flyud

• Ivan Franko National University of Lviv, Lviv,
• Opole University of Technology, Opole,

Identyfikatory

DOI

10.1515/math-2017-0030