Mathematical Modelling in Piecewise-Uniform Invironment Based on the Solution of the Markushevich Boundary Problem in the Class of Automorphic Functions

Abstract

An algorithm for the explicit solution of the Markushevich boundary value problem in the class of automorphic functions with respect of Fuchsian group $\Gamma$ of the second kind is suggested. The boundary condition of the problem is given on the main circle. The coefficients of the tasks are Holder functions. The alqorithm is based on a reduction of the problem to the Hilbert boundary problem. The solution is found in a closed form under additional restriction on the coefficient $b(t)$ of the problem: if $\chi_{+}(t), \chi_{-}(t)$ are factorization multipliers of coefficient $a(t)$, the product of the function $b(t)$ on the quotient of $\overline{\chi_{+}(t)}$ and $\chi_{+}(t)$ is analytic in the domain $D_{-}$ and automorphic with respect to $\Gamma$ in this the domain.