Asymptotic Behavior Of Bipolar Quantum Drift-Diffusion Equation

This dissertation considers the asymptotic behavior of solutions to the one-dimensional bipolar quantum drift-diffusion equation and the three-dimensional bipolar quantum drift-diffusion equation.This bipolar quantum drift-diffusion equation is coupled by an elliptic parabolic equation,and it can be used to describe the motion of charged particles in a semiconductor device or plasma.We first consider the asymptotic behavior of the solution of the one-dimensional bipolar quantum drift-diffusion equation on the half-space.Its asymptotic behavior is represented by the corresponding diffusion wave.Secondly,we consider the large-time behavior of the solution to the initial value problem of the three-dimensional bipolar quantum drift-diffusion equation.That is,we prove the overall existence of the solution of the three-dimensional bipolar quantum drift-diffusion equation,and when the time t is sufficiently large,its solution tends to a planar diffusion wave with an algebraic decay rate.Proof of these conclusions is obtained by the method of energy estimation.