标题： 时间分数阶热方程中确定时变主系数的反问题 显示英文标题

标题： Inverse problem of determining time-dependent leading coefficient in the time-fractional heat equation

摘要： 在本文中，我们研究正算子的时间分数阶热方程带有时间依赖的扩散系数的直接和反问题。 首先，我们考虑直接问题，并建立了广义解的唯一存在性。 我们还推导了一些正则性结果。 在这里，我们的证明基于本征函数展开方法。 其次，我们考虑确定扩散系数的反问题。 通过将该反问题转化为扩散系数的算子方程，展示了该反问题的适定性。 显示英文摘要

摘要： In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent diffusion coefficient for positive operators. First, we consider the direct problem, and the unique existence of the generalized solution is established. We also deduce some regularity results. Here, our proofs are based on the eigenfunction expansion method. Second, we consider the inverse problem of determining the diffusion coefficient. The well-posedness of this inverse problem is shown by reducing the problem to an operator equation for the diffusion coefficient.