Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

2018 ◽  
Vol 59 (6) ◽  
pp. 061503 ◽  
Author(s):  
Runzhang Xu ◽  
Xingchang Wang ◽  
Yanbing Yang ◽  
Shaohua Chen
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Damped Wave Equation ◽  
Nonlinear Damped Wave Equation

scholarly journals Nonlinear damped wave equation: Existence and blow-up

2017 ◽  
Vol 74 (12) ◽  
pp. 3024-3041 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Ala A. Talahmeh ◽  
Jamal H. Al-Smail
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Damped Wave Equation ◽  
Nonlinear Damped Wave Equation

Existence and blow-up of a new class of nonlinear damped wave equation

2020 ◽  
Vol 38 (3) ◽  
pp. 2649-2660
Author(s):  
Zakia Tebba ◽  
Salah Boulaaras ◽  
Hakima Degaichia ◽  
Ali Allahem
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Damped Wave Equation ◽  
New Class ◽  
Nonlinear Damped Wave Equation

scholarly journals Blow-Up of Solutions for a Class of Sixth Order Nonlinear Strongly Damped Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huafei Di ◽  
Yadong Shang
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Finite Time ◽  
Nonlinear Term ◽  
Blow Up ◽  
Sixth Order ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

We consider the blow-up phenomenon of sixth order nonlinear strongly damped wave equation. By using the concavity method, we prove a finite time blow-up result under assumptions on the nonlinear term and the initial data.

On the blow-up of solutions of a convective reaction diffusion equation

1993 ◽  
Vol 123 (3) ◽  
pp. 433-460 ◽  
Author(s):  
J. Aguirre ◽  
M. Escobedo
Keyword(s):  
Positive Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Scalar Function ◽  
Reaction Diffusion Equation ◽  
Semilinear Parabolic Equation ◽  
The Cauchy Problem ◽  
Image Position

SynopsisWe study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equationwhere u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time; (b) if 1 < q ≦ p ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.

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