The inverse problem for the Lavrent’ev–Bitsadze equation connected with the search of elements in the right-hand side

We consider an equation of mixed elliptic-hyperbolic type, whose right-hand side represents a product of two one-dimensional functions. We establish a criterion for the unique solvability of this equation and construct its solution as a sum of series on the set of its eigenfunctions. Under certain constraints imposed on the ratio of the rectangle sides, on boundary functions, and on known multipliers in the right-hand side of the equation, we obtain estimates separating small denominators that appear in coefficients of constructed series from zero.

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