A Sharp Estimate of Entropy Solution to Euler-Poisson System for Semiconductors in the Whole Domain

In this paper, we are concerned with the global existence, large time behavior, and timeincreasing-rate of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. When the adiabatic index γ > 2, the L∞ estimates of artificial viscosity approximate solutions are obtained by using entropy inequality and maximum principle. Then the L∞ compensated compactness framework demonstrates the
convergence of approximate solutions. Finally, the global entropy solutions are proved to decay exponentially fast to the stationary solution, without any assumption on the smallness of initial data and doping profile.