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 Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

2011 ◽  
Vol 74 (18) ◽  
pp. 6933-6949 ◽  
Author(s):  
Le Xuan Truong ◽  
Le Thi Phuong Ngoc ◽  
Alain Pham Ngoc Dinh ◽  
Nguyen Thanh Long
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Exponential Decay ◽  
Nonlinear Wave Equation ◽  
Blow Up ◽  
Decay Estimates ◽  
Point Type

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 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 Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Daewook Kim ◽  
Dojin Kim ◽  
Keum-Shik Hong ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Global Solutions ◽  
Growth Conditions ◽  
Decay Rates ◽  
Decay Estimates ◽  
Nonlinear Dissipation ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Energy Decay Rates

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipationg. Lastly, numerical simulations in order to verify the analytical results are given.

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