Abstract
In recent years, developed an interest in the study of boundary value problems for equations of mixed type in rectangular areas. This method proved theorems on the unique solubility and stability of the Dirichlet problem [1 – 3] under certain restrictions on the aspect ratio of the rectangular region of the hyperbolic. In this paper, for the mixed type equation with the Lavrent’ev-Bitsadze Dirichlet problem in a rectangular area. The criterion of uniqueness of the solution of the Dirichlet problem. The solution is built as the sum of the Fourier series. In justifying the convergence of a problem of small denominators regarding the relationship of the parties of the hyperbolic part of the rectangle. In connection with this evaluation are set to secede from scratch small denominator corresponding to the asymptotic behavior of rational and irrational values of the ratio, which allowed to substantiate the convergence of the series constructed in the class of regular solutions.
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