A wave equation associated with mixed nonhomogeneous conditions: Global existence and asymptotic expansion of solutions

2007 ◽  
Vol 66 (7) ◽  
pp. 1526-1546 ◽  
Author(s):  
Nguyen Thanh Long ◽  
Vo Giang Giai
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Global Existence ◽  
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.

scholarly journals Linear Approximation and Asymptotic Expansion of Solutions for a Nonlinear Carrier Wave Equation in an Annular Membrane with Robin-Dirichlet Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-18
Author(s):  
Le Thi Phuong Ngoc ◽  
Le Huu Ky Son ◽  
Tran Minh Thuyet ◽  
Nguyen Thanh Long
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Weak Solution ◽  
Small Parameter ◽  
Existence And Uniqueness ◽  
Linearization Method ◽  
Carrier Wave ◽  
Dirichlet Conditions ◽  
Asymptotic Expansion Of Solutions ◽  
Annular Membrane

This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.

On the global existence and asymptotic behavior of the solution of a nonlinear wave equation with past history

2021 ◽  
Vol 62 (3) ◽  
pp. 031512
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Mohammad Kafini ◽  
Shadi Al-Omari
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Past History
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