<p>The study presents optimal mathematical models in the context of system analysis problems. Namely, non-trivial boundary conditions are applied to the problem of integrating polyharmonic equations in polar coordinates. The function, which is triharmonic in a unit disk, is presented as an integral with a delta-like kernel. The existence of a structural relationship between the solutions to the triharmonic equations in polar coordinates and positive operators, which are solutions to other partial differential equations, is considered. It is shown that the triharmonic Poisson integral for a unit disk can be represented as the mean value of the solution to the Laplace equation in polar coordinates.</p>