We consider the Cauchy problem for an implicit system of linear partial differential equations. It belongs to the class of pseudohyperbolic systems. We prove the unique solvability of the Cauchy problem in weighted Sobolev spaces and obtain energy estimates of the solution.

中文翻译：

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拟双曲系统的柯西问题的可解性

我们考虑线性偏微分方程的隐式系统的柯西问题。它属于伪双曲系统类。我们证明了柯西问题在加权Sobolev空间中的独特可解性，并获得了该解决方案的能量估计。