応用解析セミナー

過去の記録 ~06/24次回の予定今後の予定 06/25~

開催情報 木曜日 16:00~17:30 数理科学研究科棟(駒場) 002号室
担当者 石毛 和弘

2024年05月23日(木)

16:00-17:30   数理科学研究科棟(駒場) 128号室
Adina Ciomaga 氏 (University Paris Cité (Laboratoire Jacques Louis Lions), France “O Mayer” Institute of the Romanian Academy, Iasi, Roumania)
Homogenization of nonlocal Hamilton Jacobi equations (English)
[ 講演概要 ]
I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.