Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simulation

We discuss strong solutions of a nonlinear parabolic system that arise from the simulation for the semiconductor device design. This equation considered here is governing the electron and positive hole dynamics on the MOS FET for the Large Scaled Integral-Circuit (V-LSI). We show that the existence and uniqueness and stability of the strong solution in Lp spaces and will discuss on the global existence.