日時: 2025年3月26日 (水) 16:00-17:40
場所: 京都教育大学 1A402教室 (Zoom同時配信)
16:00-16:45
講演者: Chiara Gavioli 氏 (Czech Technical University, Praha)
題目: A fractional Cahn-Hilliard problem
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain and complemented with homogeneous Dirichlet boundary conditions, and show how to prove the existence of weak solutions in a very elegant and simple way. The proof is based on the variational method known as the minimizing movements scheme, which fits naturally with the gradient-flow structure of the equation.
16:55-17:40
講演者: Chiara Gavioli 氏 (Czech Technical University, Praha)
題目: Existence results for Cahn-Hilliard-type systems driven by nonlocal integrodifferential operators with singular kernels
The interest of the method proposed in the first part of the talk lies in its extreme generality and flexibility. In particular, relying on the variational structure of the equation, we can prove the existence of a solution also for a more general class of integrodifferential operators, not necessarily linear or symmetric, which include fractional versions of the p-Laplacian. Moreover, adapting the argument to the case of regional fractional operators, we can prove the existence of solutions also in the interesting case of homogeneous fractional Neumann boundary conditions.
This is a joint work with E. Davoli and L. Lombardini (TU Wien).