Georgia Institute of Technology College of Sciences

In this talk, we consider the n-dimensional bipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. In 1-D case, when the difference between the initial electron mass and the initial hole mass is non-zero (switch-on case), the stability of nonlinear diffusion wave has been open for a long time. In order to overcome this difficulty, we ingeniously construct some new correction functions to delete the gaps between the original solutions and the diffusion waves in L^2-space, so that we can deal with the one dimensional case for general perturbations, and prove the L^\infty-stability of diffusion waves in 1-D case. The optimal convergence rates are also obtained. Furthermore, based on the results of one-dimension, we establish some crucial energy estimates and apply a new but key inequality to prove the stability of planar diffusion waves in n-D case, which is the first result for the multi-dimensional bipolar hydrodynamic model of semiconductors, as we know. This is a joint work with Feimin Huang and Yong Wang.