| 日時 | 7月13日(金) 14:50--15:50 |
|---|---|
| 会場 | 福岡大学 セミナーハウス 2階 セミナー室 |
| 講師 | 藤田 安啓 氏 (富山大学・理工) |
| 題目 | Parabolic p-Laplace equation and logarithmic Sobolev inequality |
| 概要 | It is known that a hypercontractivity of a solution to a Hamilton-Jacobi equation with a parameter $p$ is equivalent to a logarithmic Sobolev inequality with this parameter $p$. In this talk, I will show that a hypercontractivity of a solution to the parabolic p-Laplace equation is equivalent to this logarithmic Sobolev inequality. |
| 日時 | 7月13日(金) 16:00--17:00 |
|---|---|
| 会場 | 福岡大学 セミナーハウス 2階 セミナー室 |
| 講師 | Jin Feng 氏 (カンザス大学) |
| 題目 | Comparison principle for a class of Hamilton-Jacobi equation in space of measures and a conjecture by Onsager |
| 概要 | In an attempt to explain large time coherent structure for 2-D vortex flows, Onsager formally calculated statistical mechanics for an associated dynamic and made some conjectures. To rigorously prove such conjecture, we can formulate and use the theory of large deviation and Hamilton-Jacobi equations in abstract spaces. In this talk, I explain a new class of optimal controlled PDE problem arising in such context and show how comparison principle for the H-J equation can be established using mass transport techniques. This is a collaborative work with co-authors. |