Approximation of a system of nonlinear Carrier wave equations by approximating the Carrier terms with their integral sums
Abstract
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.
Keyword : system of nonlinear wave equations, the helical flows of Maxwell fluid, Kirchhoff-Carrier equations, Faedo-Galerkin method, linearization method, approximating the Carrier terms
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