Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

被引：1

作者：

Golovaty, Yuriy ^{[1
]}

Flyud, Volodymyr ^{[1
,2
]}

机构：

[1] Ivan Franko Natl Univ Lviv, Lvov, Ukraine

[2] Opole Univ Technol, Opole, Poland

来源：

OPEN MATHEMATICS | 2017年 / 15卷

关键词：

Metric graph; Hyperbolic equation; Singular perturbed problem; Asymptotics; Boundary layer; SCHRODINGER-OPERATORS; LOCALIZATION; TRANSMISSION; POTENTIALS; NETWORKS; WAVES; WIRE;

D O I：

10.1515/math-2017-0030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：404 / 419

页数：16

共 50 条

[31] Asymptotics of Solutions of Linear Singularly Perturbed Optimal Control Problems with a Convex Integral Performance Index and a Cheap Control
A. R. Danilin
A. A. Shaburov
Differential Equations, 2023, 59 : 87 - 102
[32] Asymptotic behaviour of small solutions of singularly perturbed problems
Guo, ZM
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2000, 62 (03) : 435 - 443
[33] Solutions, concentrating on spheres, to symmetric singularly perturbed problems
Ambrosetti, A
Malchiodi, A
Ni, WM
COMPTES RENDUS MATHEMATIQUE, 2002, 335 (02) : 145 - 150
[34] A CLASS OF NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION
莫嘉琪
Acta Mathematicae Applicatae Sinica(English Series), 2001, (04) : 469 - 474
[35] A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differential equation
MO Jiaqi
Acta Mathematicae Applicatae Sinica, 2001, 17 (4) : 469 - 474
[36] ASYMPTOTICS OF SOLUTIONS OF THE CAUCHY PROBLEM FOR A SINGULARLY PERTURBED OPERATOR DIFFERENTIAL TRANSPORT EQUATION
Nesterov, A. V.
THEORETICAL AND MATHEMATICAL PHYSICS, 2024, 220 (02) : 1341 - 1351
[37] Asymptotics of solutions of singularly perturbed integral differential equation with rapidly decreasing kernel
Kalimbetov, B. T.
Imanbayev, N. S.
Temirbekov, M. A.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2013, 72 (04): : 55 - 63
[38] Asymptotics of solution for singularly perturbed nonlinear discrete periodic optimal control problems
Kurina, Galina
Nekrasova, Natalya
Systems Science, 2008, 34 (01): : 23 - 38
[39] On the asymptotics of the solution to a singularly perturbed hyperbolic system of equations with several spatial variables in the critical case
T. V. Pavlyuk
A. V. Nesterov
Computational Mathematics and Mathematical Physics, 2014, 54 : 462 - 473
[40] Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in RN
Albalawi, Wedad
Mercuri, Carlo
Moroz, Vitaly
ANNALI DI MATEMATICA PURA ED APPLICATA, 2020, 199 (01) : 23 - 63

← 1 2 3 4 5 →