The Multidimensional Bipolar Quantum Drift-diffusion Model
Xiuqing Chen, Yingchun Guo · Advanced Nonlinear Studies · 2008
Abstract We investigate the bipolar quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions. First, we establish the global weak solution with large initial value and periodic boundary conditions. Then we show the semiclassical limit by using new methods based on delicate interpolation estimates and compactness argument. Furthermore, when the doping profile is a constant, we find that the weak solution approaches its mean value exponentially as time increases to infinity.