标题： 时间分数阶演化方程的反源问题 显示英文标题

标题： Inverse Source Problems for the Time-Fractional Evolution Equation

摘要： 在本文中，我们研究了在时间分数阶扩散波方程中识别时间依赖和时间独立源项的直接和线性反问题，使用时间区间内部点的测量数据。 我们首先通过采用谱方法建立了直接问题解的存在性、唯一性和正则性。 然后，基于直接问题的性质，我们研究了两个反问题：一个涉及恢复时间独立的源项，另一个涉及识别源项中的时间依赖系数函数。 显示英文摘要

摘要： In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time interval. We first establish the existence, uniqueness, and regularity of the solution to the direct problem by employing the spectral method. Then, based on the properties of the direct problem, we study two inverse problems: one involving the recovery of a time-independent source term, and the other concerning the identification of a time-dependent coefficient function in the source term.