In this paper, we discuss an initial value problem for the semilinear time-fractional diffusion equation. The local well-posedness (existence and regularity) is presented when the source term satisfies a global Lipschitz condition. The unique continuation of solution and finite time blowup result are presented when the reaction terms are logarithmic functions (local Lipschitz types).

中文翻译：

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一类半线性时间分数扩散方程的适定性结果

在本文中，我们讨论了半线性时间分数阶扩散方程的初值问题。当源项满足全局Lipschitz条件时，将显示局部的适定性（存在性和规律性）。当反应项是对数函数（局部Lipschitz类型）时，将给出解的唯一延续和有限时间的爆炸结果。