京都大学 NLPDE セミナー

本年(2025年)度のセミナーの記録

4 月 11 日
Kiyeon Lee 氏 (KAIST)

4 月 18 日
Anthony Gauvan 氏 (埼玉大学)   Anthony Gauvan (Saitama University)

4 月 25 日
小杉 千春 氏 (山口大学)   Chiharu Kosugi (Yamaguchi University)


● 2025 年 4 月 11 日 (Fri) 16:00 〜 17:00
講演者
Kiyeon Lee 氏 (Korea Advanced Institute of Science and Technology (KAIST))
講演題目
Modified scattering phenomena of nonlinear dispersive equations
講演要旨
In this talk, we will discuss the modified scattering phenomena of nonlinear dispersive equations. The modified scattering phenomenon is one of the crucial features of dispersive equations in which the dispersive effect is strong. We first introduce the decay properties of some generic dispersive equations to establish the context for scattering results. We also classify the short- and long-range nonlinearities depending on these decay bounds and introduce the asymptotic behavior of long-range nonlinearity, called the modified scattering. Additionally, we describe the space-time resonance method which will play a key role in proving the modified scattering phenomena.


● 2025 年 4 月 18 日 (Fri) 16:00 〜 17:00
講演者
Anthony Gauvan 氏 (埼玉大学)
Anthony Gauvan (Saitama University)
講演題目
On the ubiquity of geometric Brascamp-Lieb data
講演要旨
The Brascamp-Lieb inequality unifies several important inequalities. A particularly important special case is the geometric Brascamp-Lieb inequality. This inequality goes back to pioneering work of Keith Ball in the 1980s in convex geometry, and it turns out to play a fundamental role in the general theory of the Brascamp-Lieb inequality. For instance, it was shown by Bennett, Carbery, Christ and Tao that a Brascamp-Lieb inequality which possesses maximizers is equivalent to a geometric Brascamp-Lieb inequality. Relying heavily on work of Garg, Gurvits, Oliveira and Wigderson, here we present another sense in which the class of geometric Brascamp-Lieb data may be considered large. This addresses a question of Bennett and Tao in their recent work on the adjoint Brascamp-Lieb inequality.
Joint work with Neal Bez and Hiroshi Tsuji.


● 2025 年 4 月 25 日 (Fri) 16:00 〜 17:00
講演者
小杉 千春 氏 (山口大学)
Chiharu Kosugi (Yamaguchi University)
講演題目
A class of energy conservation systems representing motions of the elastic curve with the compressible stress function
講演要旨
本講演では,弾性閉曲線の伸縮運動を表す beam 方程式の初期値境界値問題を考察する. 質点系におけるエネルギー保存則から導出した方程式に空間 4 階導関数項を加えた beam 方程式を扱う. 本研究の特徴は,歪みを -1 に近づけると負の方向に発散するような応力を表す関数を扱うことと,歪みに対する下からの評価が解の性質として得られる点である. 本講演では,応力を表す関数の原始関数にある仮定をした初期値境界値問題のエネルギー保存系における時間大域解の一意存在を示す. また,エネルギー散逸系における初期値境界値問題の時間大域解の一意存在に関する結果や,歪みに対する下からの評価を得る際に鍵となる補題も紹介する.


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