## On diffusion phenomena and fractional time-derivatives, Prof. Masahiro Yamamoto (the University of Tokyo)

*In many applications one can observe anomalous diffusion phenomena in heterogeneous media and more accurate analysis is essentially demanded. For example, the diffusion of contaminants in soil often indicates anomaly, which cannot be described by the classical diffusion-advection equation and we crucially need a better model equation for reasonable predictions which guarantee public safety. Among them, the evolution equations with fractional time-derivatives are calling great attention. Although there have been many researches for fractional calculus since Leibniz, serious researches for time-fractional partial differential equations have been started only recently. In particular, the author and international research teams have established the foundation for the weak solution for initial-boundary value problems and applied it to the optimal control and inverse problems. The course aims at constructing the theory for time-fractional partial differential equations, and describing the applications, so that the audience can turn to new and fruitful research areas. 1. Introduction of fractional derivatives 2. Fractional calculus 3. Definition of fractional derivatives in Sobolev spaces and properties 4.-5. Unique existence of solution to the initial −boundary value problem 6. Asymptotic behavior, maximum principle 7. Non-homogeneous boundary value problems 8. Nonlinear equations 9. Optimal control problems 10.-12. Various inverse problems*

Starting day 04/06/2019 June All Tue Thur 10:00 12:00 room 1E Pal. RM004 (except 11, 10:00 13:00 on june 18 and 20 )