Critical and sup-critical initial energy finite time blowup phenomena for the fourth-order wave equations with nonlinear strain term

2020 ◽  
Vol 198 ◽  
pp. 111873
Author(s):  
Qiang Lin ◽  
Jihong Shen ◽  
Xingchang Wang
Keyword(s):  
Fourth Order ◽  
Finite Time ◽  
Wave Equations ◽  
Initial Energy ◽  
Nonlinear Strain ◽  
Finite Time Blowup ◽  
Time Blowup

Finite-Time Blowup for Wave Equations with a Potential

2005 ◽  
Vol 36 (5) ◽  
pp. 1426-1433 ◽  
Author(s):  
Borislav Yordanov ◽  
Qi S. Zhang
Keyword(s):  
Finite Time ◽  
Wave Equations ◽  
Finite Time Blowup ◽  
Time Blowup

FINITE TIME BLOW UP OF FOURTH-ORDER WAVE EQUATIONS WITH NONLINEAR STRAIN AND SOURCE TERMS AT HIGH ENERGY LEVEL

2013 ◽  
Vol 24 (06) ◽  
pp. 1350043 ◽  
Author(s):  
JIHONG SHEN ◽  
YANBING YANG ◽  
SHAOHUA CHEN ◽  
RUNZHANG XU
Keyword(s):  
Energy Level ◽  
Fourth Order ◽  
Finite Time ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Boundary ◽  
High Energy ◽  
Source Terms ◽  
High Energy Level ◽  
Nonlinear Strain

In this paper, we study the initial boundary value problem for fourth-order wave equations with nonlinear strain and source terms at high energy level. We prove that, for certain initial data in the unstable set, the solution with arbitrarily positive initial energy blows up in finite time.

scholarly journals FINITE TIME BLOWUP FOR THE FOURTH-ORDER NLS

2016 ◽  
Vol 53 (2) ◽  
pp. 615-640 ◽  
Author(s):  
Yonggeun Cho ◽  
Tohru Ozawa ◽  
Chengbo Wang
Keyword(s):  
Fourth Order ◽  
Finite Time ◽  
Finite Time Blowup ◽  
Time Blowup
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