Article
KYUNGPOOK Math. J. 2019; 59(4): 735-769
Published online December 23, 2019
Copyright © Kyungpook Mathematical Journal.
Linear Approximation and Asymptotic Expansion associated to the Robin-Dirichlet Problem for a Kirchhoff-Carrier Equation with a Viscoelastic Term
Le Thi Phuong Ngoc, Doan Thi Nhu Quynh, Nguyen Anh Triet, Nguyen Thanh Long∗
University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam
e-mail : ngoc1966@gmail.com
Department of Fundamental sciences, Ho Chi Minh City University of Food Industry, 140 Le Trong Tan Str., Tay Thanh Ward, Tan Phu Dist., Ho Chi Minh City, Vietnam
Department of Mathematics and Computer Science, VNUHCM - University of Science, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam
e-mail : doanquynh260919@yahoo.com
Department of Mathematics, University of Architecture of Ho Chi Minh City, 196 Pasteur Str., Dist. 3, Ho Chi Minh City, Vietnam
e-mail : triet.nguyenanh@uah.edu.vn
Department of Mathematics and Computer Science, VNUHCM - University of Science, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam
e-mail : longnt2@gmail.com
Received: September 11, 2018; Accepted: March 4, 2019
In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with a viscoelastic term. 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.
Keywords: Faedo-Galerkin method, linear recurrent sequence, RobinDirichlet conditions, asymptotic expansion in a small parameter.