Green's function and Large time behavior for the 1-D compressible Euler-Maxwell system

We study Green’s function and the large time behavior of the one-dimensional Euler-Maxwell System with relaxation. Firstly, we construct the Green’s function of linearized system and obtain the optimal time decay rates of its solutions. And then, we obtain the global existence and the optimal time decay rates of solutions to the nonlinear system by using Green’s function and a suitable energy estimate.