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.
Keywords:boundary problems for analytic functions, the Markushevich boundary problem, automorphic functions.