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Mathematical Problems in Engineering
Volume 2016, Article ID 8031638, 18 pages
Research Article

Linear Approximation and Asymptotic Expansion of Solutions for a Nonlinear Carrier Wave Equation in an Annular Membrane with Robin-Dirichlet Conditions

1University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam
2Department of Fundamental sciences, Ho Chi Minh City University of Food Industry, 140 Le Trong Tan Str., Tan Phu Dist., Ho Chi Minh City, Vietnam
3Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University-Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam
4Department of Mathematics, University of Economics of Ho Chi Minh City, 59C Nguyen Dinh Chieu Str., Dist. 3, Ho Chi Minh City, Vietnam

Received 23 April 2016; Accepted 8 September 2016

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2016 Le Thi Phuong Ngoc 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.


This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.