Approximations of Euler-Maxwell systems by drift-diffusion equations through zero-relaxation limits near the non-constant equilibrium

Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of the Euler-Maxwell system through the zero-relaxation limit towards drift-diffusion equations with non-constant doping functions.We carry out the global-in-time convergence analysis by establishing uniform estimates of solutions near nonconstant equilibrium regarding the relaxation parameter and passing to the limit by using classical compactness arguments. Furthermore, we generalize the stream function method to the non-constant equilibrium case, and together with the anti-symmetric structure of the error system and an induction argument, we establish globalin-time error estimates between smooth solutions to the Euler-Maxwell system and those to the drift-diffusion system, which are bounded by some power of the relaxation parameter.