L~p-Convergence Rates Of Solutions Of The Bipolar Quantum Hydrodynamic Models For Semiconductors In The Quarter Plane

In this paper,we consider the large time asymptotic behavior of the solution for the bipolar transient quantum potential hydrodynamic model,which is a bipolar semiconductor equation with quantum potential dissipative term.we are interested in the asymptotic behavior and theL~pconvergence rate of the initial boundary value problem for the quarter plane bipolar semiconductor model with quantum potential dissipative term,by using the classical energy method and the~1decay estimates of solution for wave equation with dissipative term,we obtain theL~p(1??+?)convergence rates of the solution of the initial boundary value problem for the bipolar semiconductor model with quantum potential dissipative term asymptotically con-verge to the self-similar solutions of the nonlinear parabolic equations.The results generalize the Li(Math.Meth.Appl.Sci.36(2013),1409-1422)L~p(2??+?)convergence rates.The paper is organized as follows:In Chapter One,we introduce the research background of bipolar semiconductor model,the content arrangement,the preliminary knowledge and the main results.In Chapter Two,we introduce the asymptotic state and the main proof of theL~p(1??+?)convergence rates of the bipolar semiconductor model.