TY  - JOUR
ID  - Lian2020
LB  - Lian2020
AU  - Lian, Wei
AU  - Ahmed, Md Salik
AU  - Xu, Runzhang
TI  - Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity
ST  - Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 1
SP  - 111
EP  - 130
DO  - https://doi.org/10.7494/OpMath.2020.40.1.111
UR  - https://doi.org/10.7494/OpMath.2020.40.1.111
AB  - In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (\(E(0)\lt d\), \(E(0)=d\) and \(E(0)\gt 0\)) using potential well method. The results in this article shed some light on using potential wells to classify the solutions of the semilinear wave equation with the product of polynomial and logarithmic nonlinearity.
KW  - global existence
KW  - blow-up
KW  - logarithmic and polynomial nonlinearity
KW  - potential well
SN  - 1232-9274
ER  -