Existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary

Authors: Nguyễn Thành Long, Lê Xuân Trường,

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Publisher, magazine: ,

Publication year: 2007

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Abstract

We study the initial boundary value problems for the non-lineal wave equation where given constants and are given functions. The unknown function and the unknown boundary value satisfy the linear integral equation where are given functions satisfying some properties stated in next section. This paper consists of 2 main sections. First, we prove the existence and uniqueness for the solutions in a suitable function space. Then, for the cases we find an asymptotic expansion of solution up to order N+1

Tags: Nonlinear wave equation; linear integral equation; existence and uniqueness; asymptotic expansion