Investigation of the inverse potential problem for the contact surface
© Chorniy A.V., Dubovenko Yu.I.
The basic mathematical models of the inverse logarithm potential problem for a contact surface are analyzed. It is noted, that some parametrical dependence of the problem solution upon the active layer density and "mean depth" or contact assymptote follows from the compound media models studied but is not the principled characterization of the problem for unlimited bodies in contrast to the problem for limited ones. The non-linear integral equation for the contact surface in complex domain, which depends only on the unique parameter — the density of the disturbing layer, is explored in detail. The conditions of the equation correct solubility are established. Local theorems of uniquness, existence and stability of its solution on the certain compact set are proved.