Time-dependent inverse source problems for a pseudoparabolic equation with memory

In this paper, we deal with two inverse source problems for a pseudoparabolic equation with memory term, which in general, have important applications in various fields of science and technology such as non-Newtonian fluids, filtration, population dynamics, plasma physic, et al. However, the presence of certain additional terms in a system usually causes specific complications in mathematical point of view, both in analytical and numerical analysis, although they characterize important physical properties of media. The studied inverse problems consist of recovering a time-dependent source parameter under two types of integral overdetermination conditions. We establish the existence, uniqueness, and stability of strong solutions under suitable conditions on the data and explore numerical solutions by creating numerical algorithms and testing examples.