一类渗透率反演问题解的存在性与唯一性

本根据Thierry Bourbie et al建立的测定致密岩心的渗透率的装置，交换相应的数学模型中的边界条件和附加条件位置，得到了相应正问题的解析解．尔后，运用偏微分方程反问题中的系数反演方法，构造出了反演渗透率的关系式，在此基础上，运用不动点定理讨论了解析反演解的存在性与唯一性．反演的结果表明：只要在L端持续测量t1时间间隔，则所给的附加条件可以唯一确定渗透率．

Existence and Uniqueness of the Solution to a Class of Inverse Permeability Problem

According to the model presented by Thierry Bourbie et al 1],which can be used to measure the permeability of a core sample,we exchange the positions of the boundary condition and the additional condition,by which we can easily derive the analytical solution of the new model.Then the reversion formulation of the inverse permeability problem was constructed,by way of the methods of inverse partial differential equations.Following the above,the results of the existence and uniqueness of the inverse solution to the new inverse problem were derived,by use of contraction mapping method.The inverse theoretical result indicates that the additional condition can determine the permeability uniquely if one makes meaurement for t 1 duration at the endpoint of L.