Approximation of a system of nonlinear Carrier wave equations by approximating the Carrier terms with their integral sums

• Published in: Mathematical modelling and analysis Vol. 30; no. 2; pp. 362 - 385
• Main Authors: Ngoc, Le Thi Phuong, Dzung, Nguyen Vu, Long, Nguyen Thanh
• Format: Journal Article
• Language: English
• Published: Vilnius Gediminas Technical University 24.04.2025
• Subjects: approximating the Carrier terms; Approximation theory; Faedo-Galerkin method; Kirchhoff-Carrier equations; linearization method; Methods; Nonlinear theories; system of nonlinear wave equations; the helical flows of Maxwell fluid; Wave functions; Vietnam; Faedo-Galerkin method; linearization method; Kirchhoff-Carrier equations; approximating the Carrier terms; the helical flows of Maxwell fluid; system of nonlinear wave equations
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2025.22230

This paper is concerned with the approximation of a system of nonlinear Carrier wave equations (CEs) by approximating the Carrier terms with their integral sums. At first, under suitable conditions, the linear approximate method, the Galerkin method, and compactness arguments provide the unique existence of a weak solution (un,vn) of the problem (Pn), for each n ∈ N, for a system of nonlinear wave equations related to Maxwell fluid between two infinite coaxial circular cylinders. Next, we prove that {(un,vn)}n converges to the weak solution (u,v)of the problem for a system of CEs in a suitable function space. This proof is done by using the compactness lemma of Aubin-Lions and the method of continuity with a priori estimates. We end the paper with a remark related to open problems.