TY  - JOUR
ID  - Yanbing2019
LB  - Yanbing2019
AU  - Yanbing, Yang
AU  - Ahmed, Md Salik
AU  - Lanlan, Qin
AU  - Runzhang, Xu
TI  - Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations
ST  - Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 2
SP  - 297
EP  - 313
DO  - https://doi.org/10.7494/OpMath.2019.39.2.297
UR  - https://doi.org/10.7494/OpMath.2019.39.2.297
AB  - Global well-posedness and finite time blow up issues for some strongly damped nonlinear wave equation are investigated in the present paper. For subcritical initial energy by employing the concavity method we show a finite time blow up result of the solution. And for critical initial energy we present the global existence, asymptotic behavior and finite time blow up of the solution in the framework of the potential well. Further for supercritical initial energy we give a sufficient condition on the initial data such that the solution blows up in finite time.
KW  - fourth-order nonlinear wave equation
KW  - strong damping
KW  - blow up
KW  - global existence
SN  - 1232-9274
ER  -