二维半无穷管道上Darcy流体方程解的空间渐近性质

Spatial Asymptotic Properties of Solutions of Darcy Fluid Equation on Two-Dimensional Semi-infinite Pipe

本文考虑多孔介质中Darcy流体方程在二维半无穷管道上的空间渐近性质.运用能量分析的办法和微分不等式技术,得到了一个关于“能量函数”的微分不等式,再解此微分不等式建立了解的Phragmen-Lindelof型二择一结果.最后,在衰减的情形下我们得到了全能量的上界.另外,本文对解的增长率/衰减率做了探讨.

The spatial asymptotic properties of Darcy fluid equation in porous media on two-dimensional semi-infinite pipe is considered.By using the method of energy analysis and differential inequality technology,a differential inequality about"energy function"is obtained,and then the differ-ential inequality is solved to establish the alternative result of Phragmén-Lindelöf type.Finally,in the case of decay,we obtain the upper bound of the total energy.In addition,the growth rate/decay rate of the solution is discussed.