Institute for Mathematical Physics on Large Time Asymptotics for Drift{diiusion{poisson Systems on Large Time Asymptotics for Drift{diiusion{poisson Systems

In this paper we analyze the convergence rate of solutions of certain drift-diiusion-Poisson systems to their unique steady state. These bi-polar equations model the transport of two populations of charged particles and have applications for semiconductor devices and plasmas. When prescribing a connnement potential for the particles we prove exponential convergence to the equilibrium. Without connnement the solution decays with an algebraic rate towards a self-similar state. The analysis is based on a relative entropy type functional and it uses logarithmic Sobolev inequalities.