Decay estimates and large time behavior of solutions to the Drift-Diffusion system

Abstract

We study the drift-diffusion system arising in the semiconductor device simulation and the plasma physics. We consider the initial value problem for this system and derive the optimal Lp decay estimate of solutions by applying the time weighted Lp energy method. Furthermore, we show that the solutions approach the corresponding heat kernels as time tends to infinity. This asymptotic result is based on the optimal Lp -Lq decay estimate for the linearized problem.