二维半无穷管道上Darcy流体方程解的空间渐近性质

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

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,得到一个关于“能量函数”的微分不等式,再解此微分不等式建立解的Phragmén-Lindelöf型二择一结果.最后,在衰减的情形下得到全能量的上界.另外,对解的增长率/衰减率进行探讨.

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 differential 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.