A time-space fractional reaction-diffusion equation in a bounded and in an unbounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions is analysed.

中文翻译：

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时空非局域反应-扩散方程的全局存在与爆发

考虑了有界和无界域中的时空分数反应扩散方程。在初始数据的某些条件下，我们表明解决方案可能会在有限的时间内经历爆炸。然而，对于现实的初始条件，解在时间上是全局的。此外，分析了有界解的渐近行为。