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We are concerned with the global existence and large time behavior of entropysolutions to the one dimensional unipolar hydrodynamic model for semiconductorsin the form of Euler-Poisson equations in a bounded interval. In this paper, wefirst prove the global existence of entropy solution by vanishing viscosity andcompensated compactness framework. In particular, the solutions are uniformlybounded with respect to space and time variables by introducing modifiedRiemann invariants and the theory of invariant region. Based on the uniformestimates of density, we further show that the entropy solution converges tothe corresponding unique stationary solution exponentially in time. No anysmallness condition is assumed on the initial data and doping profile.Moreover, the novelty in this paper is about the unform bound with respect totime for the weak solutions of the isentropic Euler-Possion system.

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices