Well-posedness Of One Dimensional Isentropic Fluid Dynamics Model

In this paper, I mainly discuss a bipolar hydrodynamic model from semiconductors orplasmas. It is coupled by the Euler-system with relaxation term and the Poisson equation ofthe electric field. From the classical energy method, I discuss the well-posedness of smoothsmall solutions for the initial boundary value problem with zero boundary conditions. Iobtain the existence and uniqueness of the global smooth solutions in the half space. Mean-while, I also show when the time t large enough, the smooth solutions tend to the solutionsof the porous media equation. Namely, the solutions of the initial value problem possessdifusive phenomena.