Equipartition of energy in one dimensional wave equation $u_{tt}-u_{xx}=0 $
Suppose $g$ and $h$ have compact support and $u\in C^2(\mathbb{R}\times [0,\infty))$ solves the wave equation and $u=g$, $u_t=h$ on $\mathbb{R}\times \{t=0\}$. The kinetic energy of the wave is and th...