Stability of non-constant steady-state solutions for bipolar non-isentropic Euler-Maxwell equations with damping terms

In this article, we consider the periodic problem for bipolar non-isentropic Euler-Maxwell equations with damping terms in plasmas. By means of an induction argument on the order of the time-space derivatives of solutions in energy estimates, the global smooth solution with small amplitude was established close to a non-constant steady-state solution with asymptotic stability property. Furthermore, we obtain the global stability of solutions with exponential decay in time near the non-constant steady-states for bipolar non-isentropic Euler-Poisson equations. This phenomenon on the charge transport shows the essential relation and difference between the bipolar non-isentropic and the bipolar isentropic Euler-Maxwell/Poisson equations.