ON A NONLINEAR WAVE EQUATION WITH A NONLOCAL BOUNDARY CONDITION
LE THI PHUONG NGOC, TRAN MINH THUYET, PHAM THANH SON, NGUYEN THANH LONG
Abstract
Consider the initial-boundary value problem for the nonlinear wave equation where ; ; are given constants and are given functions. First, the existence and uniqueness of a weak solution are proved by using the Galerkin method. Next, with , we obtain an asymptotic expansion of the solution up to order in two small parameters with error .