We consider an abstract Cauchy problem with non-linear operator coefficients and prove the existence of a unique non-extendable classical solution. Under certain sufficient close-to-necessary conditions, we obtain finite-time blow-up conditions and upper and lower bounds for the blow-up time. Moreover, under certain sufficient close-to-necessary conditions, we obtain a result on the existence of a global-in-time solution independently of the size of the initial functions.

中文翻译：

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具有非矫顽力源的形式双曲方程的柯西问题的经典意义上的爆破和整体溶解度

我们考虑带有非线性算子系数的抽象柯西问题，并证明存在唯一的不可扩展的经典解。在某些足够接近必要的条件下，我们获得了有限时间的爆炸条件以及爆炸时间的上限和下限。此外，在某些足够接近必要条件的情况下，我们获得了与全局函数无关的初始时间大小的结果。