Remarks on the Semilinear Wave Equations

Md. Abu Naim Sheikh 
 

Abstract 
We study the semilinear wave equation of the form: $\vuong u+ u_t + \vert u_t \vert^{p-1} = \vert u\vert^{q-1} u$. When $1 < q \le p$, a solution exists globally in all time and when $1 < p < q$, the local solution blows up
in finite time for negative initial energy.