Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type. (2nd September 2017)

• Record Type: Journal Article
• Authors: Ngoc, Le Thi Phuong; Triet, Nguyen Anh; Ngoc Dinh, Alain Pham; Long, Nguyen Thanh
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 9(2017)
• Page Start: 1173
• Page End: 1207
• Publication Date: 2017-09-02
• Subjects: Exponential decay -- Faedo–Galerkin method -- global existence -- local existence -- nonlinear wave equation; 35L05 -- 35L15 -- 35L70 -- 37B25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1320672
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.