Weak solutions of the isothermal bipolar hydrodynamic model for semiconductors with large data

This paper is devoted to weak solutions of Cauchy problem to the isothermal bipolar hydrodynamic model with large data. The model takes the bipolar Euler-Poisson form, with electric field and relaxation terms added to the momentum equations. Using Glimm scheme to the hyperbolic part and the standard theory to the ordinary differential equations, we first construct the approximation solutions, then from the facts that the total charge is quasi-conservation, we can obtain a uniform estimate of the total variation of the electric field, which allows to prove the L ^∞ estimate of densities and velocities, and the convergence of the scheme. Then we can prove the global existence of weal solution to Cauchy problem with large data.