Geometric PDE and Applied Analysis Seminar (September 29, 2026)

Title: Strong positivity property for subdiffusion equations and applications to related inverse problems

Speaker: Prof. Yikan Liu (Kyoto University)

Abstract: The last decade has witnessed explosive developments of nonlocal PDEs especially with fractional derivatives in time. As one of the most representative properties of classical parabolic equations, maximum principles and related properties are expected to be inherited by subdiffusion equations. In this talk, we first review weak and strong maximum principles for single subdiffusion equations, and then introduce a strict positivity property for coupled subdiffusion systems under suitable cooperativeness and connectivity conditions. As an application, we discuss a related inverse source problem on determining the temporal component.