量子漂移扩散模型解的指数衰减

研究了量子漂移扩散模型解的指数衰减．该模型来自于量子流体动力学模型，是一个非线性四阶抛物型偏微分方程组，由于比较原理对于四阶偏微分方程不再成立，进而最大模估计成为本质困难．利用熵函数的方法，结合差分法，能量估计，梅造差分方程解的迭代．从而在时间增大时，得到解在L^1意义下以指数速度衰减到常定态．

Exponential Decay of Solutions for Quantum Drift-Diffuse Model

An exponential decay of solutions for quantum drift-diffuse model is studied. This model is derived from quantum hydrodynamic model of a nonlinear fourth-order partial differential system. Since the comparison principle does not hold for the fourth-order partial differential equation, the L^∞ -estimate becomes the essence of the difficulty. Applying the methods of entropy functional, semidiscretization, energy estimation and iteration, the solutions converge is obtained for constant steady-state exponential decay in the sense of L^1 norm as the time tend to infinity.