Hydrodynamic Model Of Semiconductor With Insulating Boundary Conditions And Non-zero Doping Profile

In this paper,we first study a large time behavior framework of weak entropy solutions for multi-dimensional unipolar hydrodynamic model of semiconductor:(?)with the initial boundary conditions n(x,0)=n0(x)?0,j(x,0)=j0(x)j(x,t)·n|(?)?=0,E·n|(?)?=0,where ? is an open bounded subset of Rd and n is the unit outward normal vector of ?.Then we study the global existence and asymptotic behavior of smooth solu-tions to the following multi-dimensional bipolar hydrodynamic model of semicon-ductor:(?) with the initial boundary conditions ni{x,0)=ni0(x)>0,ji(x,0)=ji0(x)ji(x,t)·n|((?)?=0,E·n|(?)?=0,i=1,2,where ? is an open bounded subset of Rd and n is the unit outward normal vector of ?.This article is divided into four chapters.In chapter one,we first introduce the concrete form for hydrodynamic model of semiconductor.Then the related studies about this model at home and abroad are summarized,and explain the main con-tents in this paper.In chapter two,we use the basic energy estimates and entropy analysis method to obtain a large time behavior framework of weak entropy so-lutions to multi-dimensional unipolar hydrodynamic model of semiconductor with insulation boundary conditions and non-zero doping profile under L2 norm.It is worth emphasizing that this conclusion only requires the prior assumption that the electron density is bounded,and does not require any small property of the initial value.At the last of this chapter,we simply introduce the existence and asymptotic behavior of the smooth solution to multi-dimensional unipolar hydro-dynamic model of semiconductor.In the third chapter,we use a similar method to obtain the L2 decay of smooth solution to multi-dimensional bipolar hydrodynam-ic model of semiconductor.Then the exponential convergence rate is obtained by the Gronwall's inequality.In chapter four,we first obtain the pure time derivative estimates of the smooth solution by the simplified symmetric hyperbolic equation,then control the space and mixed partial derivatives by using the time derivative,and we obtain the high order estimates and global existence of the smooth solution to the model.