A nonlinear wave equation associated with nonlinear boundary conditions: Existence and asymptotic expansion of solutions

2007 ◽  
Vol 66 (12) ◽  
pp. 2852-2880 ◽  
Author(s):  
Nguyen Thanh Long ◽  
Vo Giang Giai
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Asymptotic Expansion Of Solutions

scholarly journals On a Nonlinear Wave Equation Associated with Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-33 ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Le Khanh Luan ◽  
Tran Minh Thuyet ◽  
Nguyen Thanh Long
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Weak Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Taylor Expansion ◽  
The Other ◽  
Small Parameters ◽  
Compact Imbedding ◽  
Asymptotic Expansion Of Solutions

A Dirichlet problem for a nonlinear wave equation is investigated. Under suitable assumptions, we prove the solvability and the uniqueness of a weak solution of the above problem. On the other hand, a high-order asymptotic expansion of a weak solution in many small parameters is studied. Our approach is based on the Faedo-Galerkin method, the compact imbedding theorems, and the Taylor expansion of a function.

Sign in / Sign up

Export Citation Format

Share Document