## CORSO DI DOTTORATO - Masahiro Yamamoto (The University of Tokyo - INdAM visiting professor): Inverse problems and time-fractional partial differential equations

2022, Aula 1B1, 14, 20, 22, 27, 28 September (10:00-12:00) and 4, 5, 7 October (10:00-12:00)

We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems.

The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications.

For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).