Relaxation limit and global existence of smooth solutions of compressible euler-maxwell equations

Abstract

We consider smooth periodic solutions for the Euler-Maxwell equations, which are a symmetrizable hyperbolic system of balance laws. We proved that as the relaxation time tends to zero, the Euler-Maxwell system converges to the drift-diffusion equations at least locally in time. The global existence of smooth solutions is established near a constant state with an asymptotic stability property. © 2011 Society for Industrial and Applied Mathematics.