Well-Posedness of the Complex Cauchy Problem for Systems of Partial Differential Equations in Spaces of Entire Functions with Integral Metrics

study the Cauchy problem for general linear systems of complex partial differential equations in Banach spaces of entire vector functions with integral metrics. The type of exponential growth of the solution of the problem and the right-hand side of the system of differential equations with respect to the variable z may depend in a certain way on the other variable t. Necessary and sufficient conditions are obtained under which this problem is well posed solvable in a given scale of function spaces. Therefore, a description of the structure of systems of differential equations for which the Cauchy problem is well posed is given.