An Asymptotic Theory for a Class of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations with an Application to a Model of the Galloping Oscillations of Overhead Transmission Lines

W. T. van Horssen

doi:10.1137/0148075

An Asymptotic Theory for a Class of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations with an Application to a Model of the Galloping Oscillations of Overhead Transmission Lines

SIAM Journal on Applied Mathematics ◽

10.1137/0148075 ◽

1988 ◽

Vol 48 (6) ◽

pp. 1227-1243 ◽

Cited By ~ 35

Author(s):

W. T. van Horssen

Keyword(s):

Boundary Value Problems ◽

Transmission Lines ◽

Wave Equations ◽

Asymptotic Theory ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Weakly Nonlinear ◽

Overhead Transmission Lines ◽

Initial Boundary Value

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Multiple-Scale Solution of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations on the Semi-Infinite Line

SIAM Journal on Applied Mathematics ◽

10.1137/0152054 ◽

1992 ◽

Vol 52 (4) ◽

pp. 946-958 ◽

Cited By ~ 3

Author(s):

S. C. Chikwendu ◽

C. V. Easwaran

Keyword(s):

Boundary Value Problems ◽

Nonlinear Wave ◽

Wave Equations ◽

Initial Boundary ◽

Multiple Scale ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Weakly Nonlinear ◽

Infinite Line ◽

Initial Boundary Value

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Initial Boundary-Value Problems of Nonlinear Wave Equations in an Exterior Domain

Journal of the London Mathematical Society ◽

10.1112/jlms/s2-40.3.519 ◽

1989 ◽

Vol s2-40 (3) ◽

pp. 519-534 ◽

Cited By ~ 2

Author(s):

Chen Yunmei

Keyword(s):

Boundary Value Problems ◽

Nonlinear Wave ◽

Exterior Domain ◽

Wave Equations ◽

Boundary Value ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Initial Boundary Value

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The initial–boundary value problems for a class of nonlinear wave equations with damping term

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2008.08.027 ◽

2009 ◽

Vol 351 (1) ◽

pp. 1-15 ◽

Cited By ~ 15

Author(s):

Guowang Chen ◽

Bo Lu

Keyword(s):

Boundary Value Problems ◽

Nonlinear Wave ◽

Wave Equations ◽

Boundary Value ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Damping Term ◽

Initial Boundary Value

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Regular solutions of initial-boundary value problems for linear and nonlinear wave-equations. II

Mathematische Zeitschrift ◽

10.1007/bf01214944 ◽

1975 ◽

Vol 142 (2) ◽

pp. 121-130 ◽

Cited By ~ 8

Author(s):

Wolf von Wahl

Keyword(s):

Boundary Value Problems ◽

Nonlinear Wave ◽

Wave Equations ◽

Boundary Value ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Regular Solutions ◽

Linear And Nonlinear ◽

Initial Boundary Value

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Regular solutions of initial-boundary value problems for linear and nonlinear wave-equations I

manuscripta mathematica ◽

10.1007/bf01411495 ◽

1974 ◽

Vol 13 (2) ◽

pp. 187-206 ◽

Cited By ~ 3

Author(s):

Wolf von Wahl

Keyword(s):

Boundary Value Problems ◽

Nonlinear Wave ◽

Wave Equations ◽

Boundary Value ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Regular Solutions ◽

Linear And Nonlinear ◽

Initial Boundary Value

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Application of series with recurrently calculated coefficients for solving initial-boundary value problems for nonlinear wave equations

10.1063/5.0041819 ◽

2021 ◽

Author(s):

M. Yu. Filimonov ◽

N. A. Vaganova

Keyword(s):

Boundary Value Problems ◽

Nonlinear Wave ◽

Wave Equations ◽

Boundary Value ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Initial Boundary Value

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Families of exact solutions for linear and nonlinear wave equations with a variable speed of sound and their use in solving initial boundary value problems

Theoretical and Mathematical Physics ◽

10.1134/s0040577917070030 ◽

2017 ◽

Vol 192 (1) ◽

pp. 974-981 ◽

Cited By ~ 1

Author(s):

E. V. Trifonov

Keyword(s):

Exact Solutions ◽

Boundary Value Problems ◽

Speed Of Sound ◽

Wave Equations ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Initial Boundary Value Problems ◽

Variable Speed ◽

Linear And Nonlinear ◽

Initial Boundary Value

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Asymptotic behavior of solutions for initial–boundary value problems for strongly damped nonlinear wave equations

Nonlinear Analysis ◽

10.1016/j.na.2007.08.027 ◽

2008 ◽

Vol 69 (8) ◽

pp. 2492-2495 ◽

Cited By ~ 8

Author(s):

Runzhang Xu ◽

Yacheng Liu

Keyword(s):

Asymptotic Behavior ◽

Boundary Value Problems ◽

Nonlinear Wave ◽

Wave Equations ◽

Initial Boundary ◽

Nonlinear Wave Equations ◽

Asymptotic Behavior Of Solutions ◽

Initial Boundary Value Problems ◽

Initial Boundary Value ◽

Strongly Damped

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Covariant transformations of wave equations for initial‐boundary‐value problems with moving boundary conditions

Journal of Applied Physics ◽

10.1063/1.341785 ◽

1988 ◽

Vol 64 (4) ◽

pp. 1652-1656 ◽

Cited By ~ 1

Author(s):

H. E. Wilhelm

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Wave Equations ◽

Moving Boundary ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Initial Boundary Value

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Blow Up of Solutions to One Dimensional Initial-boundary Value Problems for Semilinear Wave Equations with Variable Coefficients

Journal of Partial Differential Equations ◽

10.4208/jpde.v26.n2.4 ◽

2013 ◽

Vol 26 (2) ◽

pp. 138-150 ◽

Cited By ~ 1

Author(s):

Wei Han sci

Keyword(s):

Boundary Value Problems ◽

Wave Equations ◽

Blow Up ◽

Boundary Value ◽

Initial Boundary ◽

Variable Coefficients ◽

Initial Boundary Value Problems ◽

One Dimensional ◽

Semilinear Wave Equations ◽

Initial Boundary Value

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