We obtain necessary conditions and sufficient conditions on the existence of solutions to the Cauchy problem for a fractional semilinear heat equation with an inhomogeneous term. We identify the strongest spatial singularity of the inhomogeneous term for the solvability of the Cauchy problem.

中文翻译：

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不均匀分数阶半线性热方程解的存在性

我们获得了具有不均匀项的分数半线性热方程的柯西问题解的存在性的必要条件和充分条件。我们确定了柯西问题可解性的非均匀项的最强空间奇点。