Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-Carrier type with Balakrishnan-Taylor damping-Reference-Cited by-同舟云学术

Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-Carrier type with Balakrishnan-Taylor damping

Published:2023 Issue:8 Volume:37 Page:2321-2346
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Nhan Huu¹,Nam Bui²,Ngoc Le³,Long Nguyen²

Affiliation:

1. Ho Chi Minh University of Foreign Languages and Information Technology, Su Van Hanh, Ho Chi Minh City, Vietnam

2. Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam, Ho Chi Minh City, Vietnam + Vietnam National University, Ho Chi Minh City, Vietnam + Ho Chi Minh City University of Food Industry, Ho Chi Minh City, Vietnam

3. University of Khanh Hoa, Nha Trang City, Vietnam

Abstract

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are proved. Next, an asymptotic expansion of solutions in a small parameter with high order is established. The used main tools are the linearization method for nonlinear terms together with the Faedo-Galerkin method, and the key lemmas of the expansion of high-order polynomials and the Taylor expansion for multi-variable functions.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference26 articles.

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5. B. Feng, Y.H. Kang, Decay rates for a viscoelastic wave equation with Balakrishnan-Taylor and frictional dampings, Topological Meth. Non. Anal. 54 (1) (2019) 321-343.

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