scholarly journals On a Nonlinear Wave Equation of Kirchhoff-Carrier Type: Linear Approximation and Asymptotic Expansion of Solution in a Small Parameter

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Nguyen Huu Nhan ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Weak Solution ◽  
Dirichlet Problem ◽  
Small Parameter ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Existence And Uniqueness ◽  
Linearization Method ◽  
Asymptotic Expansion Of Solution

We consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

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.

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 Global classical solutions to the Cauchy problem for a nonlinear wave equation

1998 ◽  
Vol 21 (3) ◽  
pp. 533-548 ◽  
Author(s):  
Haroldo R. Clark
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Classical Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Global Classical Solution ◽  
Global Classical Solutions ◽  
The Cauchy Problem

In this paper we consider the Cauchy problem{u″+M(|A12u|2)Au=0   in   ]0,T[u(0)=u0,       u′(0)=u1,whereu′is the derivative in the sense of distributions and|A12u|is theH-norm ofA12u. We prove the existence and uniqueness of global classical solution.

ASYMPTOTIC EXPANSION OF THE SOLUTION FOR NONLINEAR WAVE EQUATION WITH MIXED NON-HOMOGENEOUS CONDITIONS

2003 ◽  
Vol 36 (3) ◽  
pp. 683-696
Author(s):  
Thanh Long Nguyen ◽  
Pham Ngoc Dinh Alain ◽  
Ngoc Diem Tran
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation
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