Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case

This paper is concerned with the Cauchy problem of a bipolar hydrodynamic model for semiconductor device, a system of one dimensional Euler-Poisson equations with time-dependent damping effect in the critical case. The global existence and uniqueness of the solutions to the Cauchy problem are proved by the technical time-weighted energy method, when the initial perturbation around the constant states are small enough. Particularly, the algebraic time-convergence-rates for the solutions to their constant states are also derived.