Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years. However, all existing studies have assumed that the terminal time at which one takes the observation is exactly known. In this talk, we present uniqueness and stability results for three canonical inverse problems, e.g., backward problem, inverse source and inverse potential problems, from the terminal observation at an unknown time. The subdiffusive nature of the problem indicates that one can simultaneously determine the terminal time and space-dependent parameter. The analysis is based on explicit solution representations, asymptotic behavior of the Mittag-Leffler function, and mild regularity conditions on the problem data. Further, we present several one- and two-dimensional numerical experiments to illustrate the feasibility of the approach.

We study generalized Radon-type transforms involving functions and symmetric tensor fields. We show in some instances that unique continuation principle for such transforms holds and we also give explicit counterexamples where such principle does not hold.

In this talk, we will focus in an inverse problem for the fractional wave equation with a potential, which can be regarded as a special case of the peridynamics which models the nonlocal elasticity theory. We will discuss the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. This talk is prepared based on the work https://doi.org/10.1137/21M1444941