Finite time blow-up for a kind of initial-boundary value problem of semilinear damped wave equation

2016 ◽  
Vol 40 (4) ◽  
pp. 1223-1230 ◽  
Author(s):  
Ningan Lai ◽  
Silu Yin
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Finite Time ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Damped Wave Equation ◽  
Initial Boundary Value

scholarly journals Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Fosheng Wang ◽  
Chengqiang Wang
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Viscoelastic Wave Equation ◽  
Frictional Damping ◽  
Viscoelastic Wave ◽  
Initial Boundary Value

We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is “weaker,” in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong.

Blow-Up Of Solutions For The Damped Boussinesq Equation

2005 ◽  
Vol 60 (7) ◽  
pp. 473-476 ◽  
Author(s):  
Necat Polat ◽  
Doğan Kaya ◽  
H. Ilhan Tutalar
Keyword(s):  
Boundary Value Problem ◽  
Finite Time ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Initial Boundary Value

We consider the blow-up of solutions as a function of time to the initial boundary value problem for the damped Boussinesq equation. Under some assumptions we prove that the solutions with vanishing initial energy blow up in finite time

scholarly journals Blow-Up for a Stochastic Viscoelastic Lamé Equation with Logarithmic Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Amina Benramdane ◽  
Nadia Mezouar ◽  
Mohammed Sulaiman Alqawba ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Nonlinear Source ◽  
Viscoelastic Wave ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and logarithmic nonlinear source terms. We proved a blow-up result for the solution with decreasing kernel.

scholarly journals Application of Initial Boundary Value Problem on Logarithmic Wave Equation in Dynamics

2018 ◽  
Author(s):  
Shkelqim Hajrulla ◽  
Leonard Bezati ◽  
Fatmir Hoxha
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Sobolev Inequality ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Initial Boundary Value ◽  
The Galerkin Method

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

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