Global Well-posedness Of The Inital Boundary Value Problem With Non-zero Boundary Conditions To The One-dimensional Bipolar Euler-Poisson Equations

In this paper, I investigate the bipolar hydrodynamic model from semiconductors or plasmas, which takes the form of relaxation of Euler equations and Poisson equations in the electric field. By using the classical energy method, I discuss the well-posedness of smooth small solutions for the initial boundary value problem with non-zero boundary conditions. In the half space, I obtain the existence and uniqueness of the global smooth solutions. Meanwhile, I also obtain when the time t large enough, these smooth solutions tend to the solutions of the porous media equation. The solutions of the initial value problem are diffusive phenomena.