Abstract
According to the classical Cauchy-Kowalevskaya theorem, the Cauchy problem for a differential equation (or a system) in partial derivatives with analytical coefficients and analytical initial conditions possesses a solution that is analytical in the neighborhood of any point of analyticity of the initial data. Questions about the solution's continuability and, more generally, about the domain where the solution is holomorphic and also how this is related to the holomorphy domain of the initial data have for a long time remained open. One of the first results in this direction was A. Janugauskas's paper [6] (see also [5]). In it the Cauchy problem was solved globally for the differential equation
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