Abstract: We establish the global existence of smooth solutions to the Cauchy problem for the one-dimensional isentropic Euler-Poisson (or hydrodynamic) model for semiconductors for small initial data. In particular we show that, as $t\to\infty$, these solutions converge to the stationary solutions of the drift-diffusion equations. The existence and uniqueness of stationary solutions to the drift-diffusion equations is proved without the smallness assumption.
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