Abstract We provide conditions implying finite-time blowup of positive weak solutions to the semilinear equation where and are constants, is the fractional power of the Laplacian, is a fractional Brownian motion with Hurst parameter H, and is a bounded measurable function. To achieve this we investigate the growth of integrals of the form as Moreover, we provide sufficient conditions for the existence of a global weak solution of the above equation, as well as upper and lower bounds for the probability that the solution does not blow up in finite time.

中文翻译：

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分数阶噪声扰动的分数阶反应扩散方程的全局和非全局解

摘要 我们提供了条件，其中 和 是常数，是拉普拉斯算子的分数幂，是具有赫斯特参数 H 的分数布朗运动，并且是有界可测函数。为了实现这一点，我们研究了形式为 的积分的增长 此外，我们为上述方程的全局弱解的存在提供了充分条件，以及解不会爆炸的概率的上下界有限的时间。