The paper deals with a source identification problem of the anomalous diffusion equations from nonlocal final data observations where the nonlinearity probably takes values in Hilbert scales. The existence and uniqueness results are proved by establishing some estimates for resolvent operators and using the embedding theorems. We also study regularity results for this equation in terms of the Hölder continuity of mild solutions. Finally, the multi-term fractional diffusion equations with polynomial nonlinearities and the ultra-slow diffusions are considered as illustrative applications.

中文翻译：

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具有非局部条件和弱值非线性的反常扩散方程中的参数识别

本文讨论了来自非局部最终数据观测的反常扩散方程的源识别问题，其中非线性可能取希尔伯特尺度的值。通过建立求解算子的一些估计并利用嵌入定理证明了结果的存在性和唯一性。我们还根据温和解的霍尔德连续性研究了该方程的正则性结果。最后，具有多项式非线性的多项分数扩散方程和超慢扩散被视为说明性应用。