Abstract
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.
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Li, X., Wang, S. & Feng, YH. Stability of non-constant steady-state solutions for bipolar non-isentropic Euler–Maxwell equations with damping terms. Z. Angew. Math. Phys. 67, 133 (2016). https://doi.org/10.1007/s00033-016-0728-x
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DOI: https://doi.org/10.1007/s00033-016-0728-x