Existence and asymptotic expansion for a nonlinear wave equation associated with nonlinear boundary conditions

2007 ◽  
Vol 67 (6) ◽  
pp. 1791-1819 ◽  
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

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.

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