The classical Cauchy–Kovalevskaya theorem guarantees the local existence and uniqueness of the solution to the Cauchy problem for partial differential equations with analytic coefficients. However, the existence of a solution is guaranteed only in a small neighborhood. This paper studies Cauchy problems for a specific narrow class of equations, but the solution will be obtained globally. The global solution is achieved due to the fact that the equation is considered in the complex domain.

Cauchy problem, Laplace's equation, polymorphic functions, convergence of sets.

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