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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 3626543, 18 pages
https://doi.org/10.1155/2018/3626543
Research Article

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

1Dong Nai University, 4 Le Quy Don Str., Tan Hiep District, Bien Hoa City, Vietnam
2Department of Mathematics and Computer Science, VNUHCM-University of Science, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam
3University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam

Correspondence should be addressed to Nguyen Thanh Long; moc.liamg@2tngnol

Received 25 June 2017; Accepted 10 December 2017; Published 22 January 2018

Academic Editor: Filippo Cacace

Copyright © 2018 Nguyen Huu Nhan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.