Defocusing semilinear wave equation
= Defocusing semilinear wave equation
{title2=$u_{tt}-\Delta u+u|u|^{p-1}=0$}
The defocusing power-type wave equation has the conserved nonnegative energy
$$
E(u)=\int\left(\frac{|u_t|^2+|\nabla u|^2}{2}+\frac{|u|^{p+1}}{p+1}\right)dx.
$$