We consider the Cauchy problem for general linear systems of complex partial differential equations in scales of Banach spaces of vector functions of the exponential type with an integral metric. Necessary and sufficient conditions for the well-posed solvability of this problem are obtained. Thus, we describe the structure of linear systems of complex partial differential equations for which the Cauchy problem is well posed.

中文翻译：

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向量指数型函数类中复柯西问题可解的充要条件

我们考虑具有积分度量的指数型向量函数的 Banach 空间尺度的复偏微分方程的一般线性系统的柯西问题。得到了该问题适定可解性的充分必要条件。因此，我们描述了柯西问题很好提出的复偏微分方程的线性系统的结构。