On a wave equation containing nonlinear integral terms: Existence and asymptotic expansion of solutions

Thanh, Le Thi Mai; Nhan, Nguyen Huu; Ngoc, Le Thi Phuong

doi:10.22075/ijnaa.2022.25719.3106

On a wave equation containing nonlinear integral terms: Existence and asymptotic expansion of solutions

Document Type : Research Paper

Authors

Le Thi Mai Thanh ¹

Nguyen Huu Nhan ²

Le Thi Phuong Ngoc ³

¹ Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Str., Dist. 4, Ho Chi Minh City, Vietnam

² Ho Chi Minh University of Foreign Languages and Information Technology, 828 Su Van Hanh Str., Ward 13, Dist. 10, Ho Chi Minh City, Vietnam

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

10.22075/ijnaa.2022.25719.3106

Abstract

In this paper, we consider an initial-boundary problem for a wave equation containing nonlinear integral terms. By the linear approximate method associated with the Faedo-Galerkin method, the existence and uniqueness of solutions for the proposed problem are proved. Moreover, a high-order asymptotic expansion in a small parameter of the weak solution is also discussed.

Keywords

Wave equation

Faedo-Galerkin method

Recurrent sequence

Asymptotic expansion

Nonlinear integral terms