This page is for RIMS Research Project "Deepening and applications of variational problems", which is one of the project of International Joint Usage / Research Center in Research Institute for Mathematical Sciences, Kyoto University.
- Overview -
We carry out this project based on the following two subjects:
- Deepening the insight of the lack of compactness appearing in non-compact variational problems;
- Applications of variational methods to evolution equations.
In order to achieve the two subjects, we will invite two researchers from abroad for a long-term and several young researchers for a short-term, and hold the following events:
- Series of lectures;
- Three workshops;
- School mainly for young researchers.
click here for the detail of the project
Modern variational methods have a wide range of theories; the direct method, the critical point theory represented by the minimax method and the mountain pass theorem, Morse-Conley theory, and so on. These theories have been extensively studied not only in the field of partial differential equations, such as finding solutions to nonlinear elliptic partial differential equations as the stationary point of some energy functional, but also in connection with various mathematical fields, such as Riemannian geometry, symplectic geometry, mathematical physics, and so on.
We carry out this project based on the following two subjects:
- Deepening the insight of the lack of compactness appearing in non-compact variational problems;
- Applications of variational methods to evolution equations.
"Non-compact variational problem" in subject (A) is the variational problem such that the approximate sequence (such as minimizing sequence, or Palais-Smale sequence) is not always compact by itself, and it often appears in the application to the fields mentioned in the introduction. By virtue of the concentration-compactness principle, introduced by Prof. Pierre-Louis Lions in 1980s, the mechanism of the lack of compactness is generally understood and this theory has been widely applied to the study of non-compact variational problems. Subject (A) aims to refine the understanding of the mechanism and give new applications for non-compact variational problems.
Besides, by the use of the concentration-compactness principle, there are various studies of the asymptotic behavior of global-in-time solutions to nonlinear evolution equations, such as nonlinear parabolic, wave, dissipative equations. The purpose of subject (B) is to develop the study of evolution equations using variational methods, represented by these applications.
In order to achieve the two subjects, we will invite Prof. Bernhard Ruf (University of Milan) and Prof. Luca Martinazzi (University of Rome ``La Sapienza") for a long-term to give a series of lectures and hold three workshops. For subject (B), in particular, we will hold a workshop in order to identify current issues and open problems based on the progress since the RIMS workshop "Progress in Variational Problems -Variational Methods in the Study of Evolution Equations-", which was held under the same theme. In addition, we will hold a school mainly for young researchers. At these workshops and schools, we will invite young researchers from abroad for a short-term. This project will be carried out in close collaboration with the Osaka Central Advanced Mathematics Institute (OCAMI).
- Organizing Committee and Related Researchers -
Chairman of Organizing Committee
- TAKAHASHI, Futoshi
Graduate School of Science, Osaka Metropolitan University / Professor
Organizing Committee
- ISHIWATA, Michinori
Graduate School of Engineering Science, Osaka University / Professor - NAKANISHI, Kenji
Research Institute for Mathematical Sciences, Kyoto University / Professor - WADADE, Hidemitsu
Faculty of Mechanical Engineering, Institute of Science and Engineering, Kanazawa University / Associate Professor - IOKU, Norisuke
Graduate School of Science, Tohoku University / Associate Professor - NAIMEN, Daisuke
Graduate School of Engineering, Muroran Institute of Technology / Associate Professor
Researcher
- SUGURO, Takeshi
Research Institute for Mathematical Sciences, Kyoto University / Researcher
- MIYAKE, Nobuhito
(April, 2021〜March, 2022)
- Workshops and Related Seminars -
Past records
- Summer School on Variational Problems and Functional Inequalities
Period September 21-22, 2022 Location Osaka Metropolitan University, Department of Science, Large Lecture Room (E408) Program (Click here for the program) Abstract (Click here for the abstract) Invited Speakers - Bernhard Ruf (Univ. of Milan)
- Luca Martinazzi (Univ. of Rome ``La Sapienza")
- Shoichi Hasegawa (Waseda Univ.)
- Ikkei Shimizu (Osaka Univ.)
- Haoyu Li (Osaka Univ.)
- Nobuhito Miyake (Univ. of Tokyo)
- Takeshi Suguro (Kyoto Univ.)
- Naoki Hamamoto (Osaka Metropolitan Univ.)
- Workshop on Non-compact Variational Problems and Related Topics
Period September 26-28, 2022 Location Kyoto University, Research Institute for Mathematical Science, Room 420 Program (Click here for the program) Abstract (Click here for the abstract) Invited Speakers - Bernhard Ruf (Univ. of Milan)
- Luca Martinazzi (Univ. of Rome ``La Sapienza")
- Michiaki Onodera (Tokyo Institute of Technology)
- Tatsuya Miura (Tokyo Institute of Technology)
- Yohei Tsutsui (Kyoto Univ.)
- Asuka Takatsu (Tokyo Metropolitan Univ.)
- Hiroaki Kikuchi (Tsuda College)
- Masato Hashizume (Hiroshima Univ.)
- Norihisa Ikoma (Keio Univ.)
- Yoshitsugu Kabeya (Osaka Metropolitan Univ.)
- Workshop on Variational Methods and Dispersive Equations
Period February 6-8, 2023 Location Kyoto University, Research Institute for Mathematical Science, Room 420 Program (Click here for the program) Invited Speakers - Slim Ibrahim (Univ. of Victoria)
- Tetsu Mizumachi (Hiroshima Univ.)
- Mitsuru Shibayama (Kyoto Univ.)
- Ken Abe (Osaka Metropolitan Univ.)
- Masaya Maeda (Chiba Univ.)
- Yohei Yamazaki (Kyushu Univ.)
- Masaru Hamano (Waseda Univ.)
- Jun-ichi Segata (Kyushu Univ.)
- Hiroyuki Hirayama (Miyazaki Univ.)
- Koichi Komada (Chukyo Univ.)
- Workshop on Variational Methods and Functional Inequalities
Period February 13-15, 2023 Location Osaka Metropolitan University, Department of Science, Large Lecture Room (E408) Program (Click here for the program) Invited Speakers - Bernhard Ruf (Univ. of Milan)
- Luca Martinazzi (Univ. of Rome ``La Sapienza")
- Gabriele Mancini (Univ. of Bari)
- Shinji Adachi (Shizuoka Univ.)
- Satoshi Masaki (Osaka Univ.)
- Neal Bez (Saitama Univ.)
- Kazunaga Tanaka (Waseda Univ.)
- Kazuhiro Kurata (Tokyo Metropolitan Univ.)
- Megumi Sano (Hiroshima Univ.)
- Shinichiroh Matsuo (Nagoya Univ.)