On a Nonlinear Wave Equation of Kirchhoff-Carrier Type: Linear Approximation and Asymptotic Expansion of Solution in a Small Parameter-Reference-Cited by-同舟云学术

On a Nonlinear Wave Equation of Kirchhoff-Carrier Type: Linear Approximation and Asymptotic Expansion of Solution in a Small Parameter

Published:2018 Issue: Volume:2018 Page:1-18
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Nhan Nguyen Huu¹²,Ngoc Le Thi Phuong³,Long Nguyen Thanh²^ORCID

Affiliation:

1. Dong Nai University, 4 Le Quy Don Str., Tan Hiep District, Bien Hoa City, Vietnam

2. Department of Mathematics and Computer Science, VNUHCM-University of Science, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam

3. University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam

Abstract

We consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2018/3626543.pdf

Reference19 articles.

1. Mechanik,1876

2. On the non-linear vibration problem of the elastic string

3. Existence and Exponential Decay for a Kirchhoff–Carrier Model with Viscosity

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