Asymptotic Convergence And Attenuation Estimation Of Euler - Poisson Equation For High - Dimensional Unipolar Quantum

In this paper,we study the multi-dimensional unipolar quantum Euler-Poisson equation,which is conserved by mass,momentum, energy conservation.The difference between the quantum Euler-Poisson equation and the general Euler-Poisson equation is that the previous add new term12ε2n( √n√n) in the conservation of momentum. we show asymptotic behavior and exponential decay of the solutions for the initial value problem to the multi-dimensional unipolar quantum Euler-Poisson equations,when the far field states of current density are inconsistent and the far field of the electric is not zero. Based on the results that we have obtained in the third part for the1-D case, we can further show the stability of planar stationary in multi-dimensional case. Utilizing the energy method, we obtain the global existence of the solutions of the multi-dimensional unipolar quantum Euler-Poisson equations,and get the solutions asymptotic behavior and exponential decay rates.