Global Existence and Relaxation Limit for Smooth Solutions to the Euler-Poisson Model for Semiconductors

We establish the global existence of smooth solutions of the Cauchy problem for the one-dimensional Euler--Poisson model for semiconductors, under the assumption that the initial data are perturbations of a stationary solution of the drift-diffusion equations. The resulting evolutionary solutions converge asymptotically in time to the unperturbed state.

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