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 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 Existence, blow-up and exponential decay estimates for the nonlinear Kirchhoff-Carrier wave equation in an annular with nonhomogeneous Dirichlet conditions

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5561-5588 ◽  
Author(s):  
le Son ◽  
Le Ngoc ◽  
Nguyen Long
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Blow Up ◽  
Initial Energy ◽  
Decay Estimates ◽  
Carrier Wave ◽  
Dirichlet Conditions ◽  
Uniqueness Of The Solution

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annular associated with nonhomogeneous Dirichlet conditions. At first, by applying the Faedo-Galerkin, we prove existence and uniqueness of the solution of the problem considered. Next, by constructing Lyapunov functional, we prove a blow-up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak 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.

Asymptotic Expansion of Solutions of Parabolic Equations with a Small Parameter

1998 ◽  
Vol 5 (6) ◽  
pp. 501-512
Author(s):  
A. Gagnidze
Keyword(s):  
Asymptotic Expansion ◽  
Heat Equation ◽  
Small Parameter ◽  
Parabolic Equations ◽  
Finite Function ◽  
Complete Asymptotic Expansion ◽  
Asymptotic Expansion Of Solutions

Abstract The heat equation with a small parameter, is considered, where ε ∈ (0, 1), 𝑚 < 1 and χ is a finite function. A complete asymptotic expansion of the solution in powers ε is constructed.

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