Abstract:
The paper presents an algorithm for calculating the horizontal, vertical and tangential stresses
in a horizontal coal seam lying between galleries. These stresses are expressed in terms of the Airy function, which satisfies a homogeneous biharmonic equation. For its numerical solution it is necessary to set
boundary conditions. Practical limitations do not allow us to determine the tangential stresses on horizontal boundaries of the coal seam. Calculations of stresses are proposed to be carried out in two steps.
The first step is to solve the inverse problem for the biharmonic equation to find unknown tangential
stresses on horizontal boundaries of the coal seam. The inverse problem is solved by minimizing the
residual functional. Its strong convexity is proved, which implies the existence and uniqueness of the
solution of the inverse problem. The second step is to solve the boundary value problem for the bihar
