Asymptotic Behavior Of The Spherical Symmetric Solution Of A Bipolar Hydrodynamic Model For Semiconductor

In this paper, we mainly study the asymptotic behavior of spherical symmetric solutions of a bipolar hydrodynamic for semiconductor.where x ? RN(N > 2) is the space variable, t ? R+ = [0, ?) is the time variable.This paper is divided into four chapters. In chapter one, we mainly introduce the physical background and significance of the bipolar hydrodynamic model for semiconductor. Then, we summarize the relating studying results, both home and abroad. In chapter two, first of all,we obtain the spherical symmetric steady state equation of bipolar hydrodynamic for semiconductor.Then,by means of the vari-ational method,we prove the existence of spherical symmetric steady solutions of bipolar hydrodynamic model for semiconductor.And the uniqueness of minimum point is given. At the same time, we get some bounded estimations of the steady solutions. In chapter three, under the condition of smallness assumption of initial value,we prove the global existence of the smooth solution of spherical symmet-ric solutions for bipolar hydrodynamic model. We mainly use Young,s inequality to get the priori estimates of smooth solutions. And the global existence of the smooth solution can be obtained thanks to local existence theorems of solutions.In chapter four, by means of the energy method and the entropy inequality, we ob-tain the framework for any uniformly bounded spherical symmetric weak entropy solutions for bipolar hydrodynamic model. The solutions are shown to converge to the stationary solutions in the way of exponential decay.So,we get the asymptotic behavior of the spherical symmetric weak solutions of bipolar hydrodynamic for semiconductor.