摘要
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,构造差分方程解的迭代.从而在时间增大时,得到解在L1意义下以指数速度衰减到常定态.
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.
出处
《大连交通大学学报》
CAS
2009年第4期111-112,共2页
Journal of Dalian Jiaotong University
关键词
存在性
指数衰减
大时间行为
existence
exponential decay
large time behavior
