In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional derivative in time. Theoretically, we prove a novel conditional Lipschitz stability result, and numerically, we develop an easy-to-implement fixed point iteration for recovering the unknown coefficient. In addition, we establish rigorous error bounds on the discrete approximation. These results are obtained by crucially using smoothing properties of the solution operators and suitable choice of a weighted $L^p(0,T)$ norm. The efficiency and accuracy of the scheme are showcased on several numerical experiments in one- and two-dimensions.

翻译：本文研究从解在区域上的积分测量中恢复半线性亚扩散模型中时间依赖势的反问题。该模型涉及时间上的Djrbashian--Caputo分数阶导数。理论上，我们证明了新颖的条件Lipschitz稳定性结果；数值上，我们开发了一种易于实现的固定点迭代方法用于恢复未知系数。此外，我们建立了离散近似上的严格误差界。这些结果的关键在于利用解算子的光滑性质以及适当加权的$L^p(0,T)$范数选择。该方案的效率和精度通过一维和二维中的多个数值实验得到展示。