Hyperbolic PDEs

Let $E=(E^1, E^2, E^3)$ be the electric field and $B=(B^1, B^2,B^3)$ be the magnetic field satifying the Maxwell's equations: Show that the components of the electric and magnetic fields satisfy the...

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...