大学校案内
教員紹介
百名 亮介Hyakuna Ryosuke
【准教授】能力開発基礎系／技術基礎ユニット
| 学位 | 博士（理学） 早稲田大学、2012 |
|---|---|
| 学歴 | 早稲田大学大学院理工学研究科博士課程修了、2011 |
| メールアドレス | r-hyakuna[$]uitec.ac.jp |
| 専門分野 | 数学、偏微分方程式 |
ユニット研究と教員研究の関連性
数学系基礎教育科目を担当する。
私の教育方針
確かな基礎科学の知識と素養をもって、科学・技術・技能の最先端で活躍できる人材を育成すること。
主な研究実績等
1）主要論文
- 学術論文等
[10] R. Hyakuna, Well-posedness for the 1D cubic nonlinear Schr\"odinger equation in L^p, p>2, Nonlinear Analysis Theory, Methods & Applications 74 (2023), 113154. DOI 10.1016/j.na.2022.113154
[9] R. Hyakuna, Local and Global well-posedness, and L^p'-decay estimates for 1D nonlinear Schrodinger equations with Cauchy data in L^p, Journal of Functional Analysis, 278 (2020), 108511. DOI 10.1016/j.jfa.2020.108511
[8] R. Hyakuna, On the global Cauchy problem for the Hartree equation with rapidly
decaying initial data, Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire,
36(4) (2019), 1081--1104. DOI 10.1016/j.anihpc.2018.11.004
[7] G.Hoshino and R. Hyakuna, Trilinear L^p estimates with applications to the Cauchy problem for the Hartree-type equation, Journal of Mathematical Analysis and Applications 469 (2019), 321--341. DOI 10.1016/j.jmaa.2018.09.014
[6] R. Hyakuna, Global solutions to the Hartree equation for large L^p-initial data, Indiana University Mathematics Journal, 68(2019), no.4, 1149--1172. DOI 10.1512/iumj.2019.68.7740
[5] R. Hyakuna, Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in $\widehat{L^p}$-spaces, Journal of Evolution Equations, 18(3), (2018), 1069--1084. DOI 10.1007/s00028-018-0432-8
[4] G. Hoshino and R. Hyakuna, Analytic Smoothing effect for the Nonlinear Schrodinger equations without square integrability, Journal of Fourier Analysis and Applications, 24(4), (2018), 321--341. DOI 10.1007/s00041-017-9562-6
[3] R. Hyakuna and M. Tsutsumi, On existence of global solutions of Schrödinger equations with subcritical nonlinearity for $\widehat{L^p}-initial data, Proceedings of the American Mathematical Society (2012), Volume 140, Number 11, 3905--3920. DOI 10.1090%2FS0002-9939-2012-11314-0
[2] R. Hyakuna and M. Tsutsumi, On the global wellposedness for the nonlinear Schrödinger equations with $L^p$ -large initial data, Nonlinear Differential Equations and Applications NoDEA 18 (2011), 309--327. DOI 10.1007/s00030-011-0097-2
[1] R. Hyakuna, T. Tanaka and M. Tsutsumi, On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite L2 norm, Nonlinear Analysis TMA, 74(2011),1304--1319. DOI 10.1016/j.na.2010.10.003 - 本校論文
- 学会発表・講演等
・Cauchy problem for nonlinear Schrödinger equations with rapidly decaying data, Workshop on Hyperbolic and Dispersive PDEs in
Fukuoka, 九州大学. 2018年2月.
・On the Cauchy problem of nonlinear Schrödinger equations in non-L^2-based spaces, Workshop on linear and nonlinear dispersive equations and related topics, Kansai seminar house, Kyoto. 2017年5月.
・Local well-posedness for the nonlinear Schrödinger equation in one space dimension, International workshop on “Fundamental problems on Theoretical and Mathematical Physics”, Waseda University. 2016年7月.
・On the Cauchy problem for the Nonlinear Schrödinger equation with initial data with infinite $L^2$ norm, AIMS 2016 Meeting, Orland, Florida, USA. 2016年7月.
・Well-posedness of nonlinear Schrödinger equations for initial data with infinite $L^2$ norm, 第597回応用解析研究会, 早稲田大学. 2015年4月.
・$L^p$-型のノルムをもつ初期値に対する非線形シュレディンガー方程式の可解性について, 東北大学応用数学セミナー, 東北大学. 2014年5月.