Numerical Solution of Robin-Dirichlet Problem for a Nonlinear Wave Equation with Memory Term

2021 ◽  
pp. 178-191
Author(s):  
Le Thi Mai Thanh ◽  
Tran Trinh Manh Dung ◽  
Nguyen Huu Nhan
Keyword(s):  
Wave Equation ◽  
Dirichlet Problem ◽  
Numerical Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Memory Term ◽  
With Memory

scholarly journals General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Salah Boulaaras ◽  
Fares Kamache ◽  
Youcef Bouizem ◽  
Rafik Guefaifia
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Lyapunov Functional ◽  
Blow Up ◽  
Initial Energy ◽  
General Decay ◽  
Memory Term ◽  
Decay Of Solutions ◽  
With Memory

AbstractThe paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow-up of solutions with nonpositive initial energy.

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.

Existence and exponential decay of the Dirichlet problem for a nonlinear wave equation with the Balakrishnan–Taylor term*

2020 ◽  
Vol 60 (2) ◽  
pp. 225-247
Author(s):  
Le Thi Phuong Ngoc ◽  
Nguyen Huu Nhan ◽  
Bui Duc Nam ◽  
Nguyen Thanh Long
Keyword(s):  
Wave Equation ◽  
Dirichlet Problem ◽  
Nonlinear Wave ◽  
Exponential Decay ◽  
Nonlinear Wave Equation ◽  
Taylor Term
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