First, by a probabilistic approach through the Feynman-Kac representation, we obtain a sufficient condition for the blow up in infinite time of the positive solution of a nonlinear anomalous reaction-diffusion system. Afterward, by reducing our system to an ordinary differential system, we prove that, in fact, our condition implies blow up in finite time of the solution.

中文翻译：

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非线性反常反应-扩散系统解的爆破

首先，通过 Feynman-Kac 表示的概率方法，我们获得了非线性异常反应扩散系统的正解在无限时间内爆炸的充分条件。然后，通过将我们的系统简化为一个普通的微分系统，我们证明，事实上，我们的条件意味着在有限时间内解决方案的爆炸。