Updated on 2023/11/05

写真a

 
KIKUCHI, Hiroaki
 
Organization
College of Liberal Arts Department of Mathematics Professor
Title
Professor

Research History

  • Tsuda University   Faculty of Liberal Arts Department of Mathematics   Professor

    2021.4

  • Tsuda University   Faculty of Liberal Arts Department of Mathematics   Associate Professor

    2015.4 - 2021.3

  • Tsuda University   Faculty of Liberal Arts Department of Mathematics   Assistant Professor

    2012.4 - 2015.3

 

Papers

  • Pitchfork bifurcation at line solitons for nonlinear Schr¥"{o}dinger equations on the product space $¥mathbb{R} ¥times ¥mathbb{T}$ Reviewed International coauthorship

    Takafumi Akahori, Yakine Bahri, Slim Ibrahim and Hiroaki Kikuchi

    Annales Henri Poincare   2023

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    Language：English   Publishing type：Research paper (scientific journal)  


    In this paper, we study the bifurcation problem from a line soliton
    for a stationary nonlinear Schr¥"{o}dinger equation on the product space $¥R ¥times ¥T$. We extend earlier results to a larger class of the nonlinearity in the equation. The salient point of our analysis relies on a lower bound of solution to the ``auxiliary equation'' and then on the application of the Crandall-Rabinowitz argument.

  • Threshold solutions for the 3D focusing cubic-quintic nonlinear Schrodinger equation at low frequencies Reviewed

    Masaru Hamano, Hiroaki Kikuchi and Minami Watanabe

    Dynamics of Partial Differential Equations   20 ( 4 )   263 - 297   2023

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    This paper addressesthe focusing cubic-quintic nonlinear Schr\"{o}dinger equation in three space dimensions. Especially, we study the
    global dynamics of solutions whose energy and mass equal to those of
    the ground state in the spirits of
    Duyckaerts and Merle (2009).
    When we try to obtain the corresponding results of Duyckaerts and Merle (2009), we meet several difficulties due to the cubic-quintic nonlinearity.
    We overcome them by using the one-pass theorem (no return theorem) developed by Nakanishi and Schlag (2012).

    DOI： 10.4310/DPDE.2023.v20.n4.a1

  • Non-existence of ground states and gap of variational values for 3D Sobolev critical nonlinear scalar field equations. Reviewed International coauthorship

    Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Hayato Nawa

    Journal of Differential Equations   334 ( 15 )   25 - 86   2022.10

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1016/j.jde.2022.06.016

  • Global dynamics above the ground state energy for the combined power-type nonlinear Schrödinger equations with energy-critical growth at low frequencies Reviewed International coauthorship

    Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Hayato Nawa

    Memoirs of the American Mathematical Society   272 ( 1331 )   1 - 130   2021.7

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1090/memo/1331

  • Transverse stability of line soliton and characterization of ground state for wave guide Schrödinger equations Reviewed International coauthorship

    Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi

    Journal of Dynamics and Differential Equations   33 ( 3 )   1297 - 1339   2021.1

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1007/s10884-020-09937-1

  • Non-uniqueness for an energy-critical heat equation on R^2 Reviewed

    380   317 - 348   2021

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1007/s00208-020-01961-2

  • Remarks on solitary waves and Cauchy problem for half-wave-Schrödinger equations Reviewed

    Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi

    Communications in Contemporary Mathematics   23 ( 5 )   1 - 31   2021

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1142/S0219199720500583

  • Existence of a ground state and blowup problem for a class of nonlinear Schrödinger equations involving mass and energy critical exponents.

    Hiroaki Kikuchi, Minami Watanabe

    Nonlinear Differential Equations and Applications   2020.10

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1007/s00030-020-00660-w

  • Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies Reviewed

    Takafumi Akahori, Slim Ibrahim, Norihisa Ikoma, Hiroaki Kikuchi, Hayato Nawa

    Calculus of Variations and Partial Differential Equations   58 ( 4 )   1 - 32   2019.6

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  • Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter Reviewed

    Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi

    Proceedings of the Royal Society of Edinburgh Section A: Mathematics   2019.5

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  • Bifurcation diagram of solutions to elliptic equation with exponential nonlinearity in higher dimensions Reviewed

    Hiroaki Kikuchi

    Proceedings of the Royal Society of Edinburgh Section A: Mathematics   2018.4

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  • Virial functional and dynamics for nonlinear Schrödinger equations of local interactions Reviewed

    25 ( 1 )   1 - 27   2018.4

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： https://doi.org/10.1007/s00030-018-0497-7

  • Remarks on scattering problem for a class of nonlinear Schrödinger equations Invited Reviewed

    Hiroaki Kikuchi

    RIMS Kôkyûroku Bessatsu   B70   73 - 92   2018

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

  • Existence of a ground state and scattering for a nonlinear Schr\"{o}dinger equation with critical growth Reviewed

    Takafumi Akahori. Slim Ibrahim. Hiroaki Kikuchi. Hayato Nawa.

    Selecta Mathematica   19   545 - 609   2013.12

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    Language：English   Publishing type：Research paper (scientific journal)  

  • Existence and uniqueness of singular solution to stationary Schr\"{o}dinger equation with supercritical nonlinearity. Reviewed

    Fouad Hadj Selem, Hiroaki Kikuchi and Juncheng Wei

    Discreat and Continuous Dynamical Systems-series A   33 ( 10 )   4613 - 4626   2013.10

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

  • Scattering and blowup problems for a class of nonlinear Schr\"{o}dinger equations Reviewed

    Takafumi Akahori. Hiroaki Kikuchi. Hayato Nawa.

    Differential and Integral Equations   25   1075 - 1118   2012.11

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    Language：English   Publishing type：Research paper (scientific journal)  

  • Stationary problem related to nonlinear Schr\"{o}dinger equations on the unit ball. Reviewed

    Reika Fukuizumi. Fouad Hadj Selem. Hiroaki Kikuchi.

    Nonlinearity   25 ( 8 )   2271 - 2301   2012.8

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  • Existence of a ground state and blow-up problem for a nonlinear Schrödinger equation with critical growth.

    Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi and Hayato Nawa

    Differential and Integral Equations. 25 (2012)   383 - 402   2012.1

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  • Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities

    Fouad Hadj Selem,Hiroaki Kikuchi

    Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities,   746 - 754   2012.1

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    Language：English   Publishing type：Research paper (scientific journal)  

  • Orbital stability of semitrivial standing waves for the Klein-Gordon-Schrödinger system,

    Hiroaki Kikuchi

    Annales de l'Institut Henri Poincare-AN. 28 (2011)   315 - 323   2011.1

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    Language：English   Publishing type：Research paper (scientific journal)  

  • Remarks on the orbital instability of standing waves for the wave-Schrödinger system in higher dimensions

    Hiroaki Kikuchi

    Communication Pure Applied Analysis   9 ( 2 )   351 - 364   2010.1

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    Language：English   Publishing type：Research paper (scientific journal)  

  • Stable standing waves for the two-dimensional Klein-Gordon-Schrödinger system

    Hiroaki Kikuchi

    Proceeding Royal Society. Edinburgh Section A.   140 ( 05 )   1011 - 1039   2010.1

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  • Stability of standing waves for the Klein-Gordon-Schrödinger system

    Hiroaki Kikuchi,Masahito Ohta

    Journal of Mathematical Analysis and Applications   ( 365 )   109 - 114   2010.1

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  • Instability of standing waves for the Klein-Gordon-Schrödinger system

    Hiroaki Kikuchi,Masahito Ohta

    Hokkaido Mathematical Journal   37 ( 4 )   735 - 748   2008.1

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  • On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations

    Hiroaki Kikuchi

    Nonlinear Analysis 67 (2007)   1445 - 1456   2007.1

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  • Existence and stability of standing waves for Schrödinger-Poisson-Slater equation

    Hiroaki Kikuchi

    Advanced Nonlinear Studies 7 (2007)   403 - 437   2007.1

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Presentations

  • Uniqueness of ground states for double power nonlinear Schrodinger equations

    2023.3.7 

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    Event date： 2023.3.6 - 2023.3.8

    Language：Japanese   Presentation type：Oral presentation (general)  

    Country：Japan  

  • Threshold solutions for the 3D focusing cubic-quintic nonlinear Schrodinger equation Invited International conference

    The 24th Northeastern Symposium on Mathematical Analysis  2023.2.20 

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    Event date： 2023.2.20 - 2023.2.21

    Language：English   Presentation type：Oral presentation (invited, special)  

    Country：Japan  

  • Uniqueness of ground states for double power nonlinear Schrödinger equations Invited

    2022.9.26 

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    Event date： 2022.9.26 - 2022.9.28

    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：京都大学数理解析研究所   Country：Japan  

  • 空間３次元における二重べき非線形シュレディ ンガー方程式の基底状態 Invited International coauthorship

    菊池弘明

    日本数学会2022年度秋季総合分科会  2022.9.15 

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    Event date： 2022.9.13 - 2022.9.16

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：北海道   Country：Japan  

  • 二重べき非線形シュレディンガー方程式の基底状態の非退化性について Invited

    菊池弘明

    NLPDE Spring セミナー  2022.3.14 

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    Event date： 2022.3.14

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：京都大学数学教室   Country：Japan  

  • Nondegeneracy of ground states for double power nonlinear Schr\"odinger equations

    2022.3.8 

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    Event date： 2022.3.7 - 2022.3.8

    Language：Japanese   Presentation type：Oral presentation (general)  

    Country：Japan  

  • Construction of a bifurcation branch from line solitons for nonlinear Schrodinger equations on product space Invited

    2022.2.17 

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    Event date： 2022.2.17 - 2022.2.18

    Language：Japanese   Presentation type：Oral presentation (general)  

    Country：Japan  

  • Construction of bifurcation branch from line solitons for nonlinear Schrodinger equations on product space ℝ × 𝕋 Invited International coauthorship

    2021.10.16 

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    Event date： 2021.10.16

    Language：Japanese   Presentation type：Oral presentation (general)  

    Country：Japan  

  • Construction of a bifurcation branch from line solitons for nonlinear Schrodinger equations on product space International coauthorship

    2021.8.31 

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    Event date： 2021.8.30 - 2021.8.31

    Language：Japanese   Presentation type：Oral presentation (general)  

    Country：Japan  

  • R. Killip, J. Murphy and M. Visan Cubic-quintic NLS: scattering beyond the virial threshold (preprint) の論文紹介 Invited

    菊池弘明

    京都大学数理解析研究所　共同研究「線形および非線形分散型方程式の研究の進展」  2021.5.18 

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    Event date： 2021.5.17 - 2021.5.20

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：京都大学数理解析研究所   Country：Japan  

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions Invited

    2021.1.15 

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    Event date： 2021.1.15

    Language：Japanese   Presentation type：Oral presentation (general)  

    Country：Japan  

  • Existence of a ground state and blowup problem for a class of nonlinear Schr ̈odinger equations Invited International conference

    Hiroaki Kikuchi

    2020 CMS Winter Meeting (session Nonlinear PDEs and kinetic problems)  2020.12.4  Slim Ibrahim Weiran Sun

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    Event date： 2020.12.4 - 2020.12.5

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Online   Country：Canada  

    Other Link： https://winter20.cms.math.ca

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions

    菊池弘明

    広島数理解析セミナー 

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    Event date： 2019.12.6

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：広島大学  

  • Non-uniqueness for an energy-critical heat equation on R^2

    菊池弘明

    応用数理解析セミナー 

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    Event date： 2019.10.31

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：東北大学  

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions

    菊池弘明

    第30回さいたま数理解析セミナー 

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    Event date： 2019.9.23

    Language：Japanese   Presentation type：Oral presentation (general)  

  • Non-uniqueness for an energy-critical heat equation on R^2

    菊池弘明

    愛媛大学における微分方程式セミナー 

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    Event date： 2019.8.23

    Language：Japanese   Presentation type：Oral presentation (general)  

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions

    菊池弘明

    第164回神楽坂解析セミナー 

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    Event date： 2019.7.27

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：東京理科大  

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions

    菊池弘明

    九州関数方程式セミナー 

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    Event date： 2019.7.12

    Language：Japanese   Presentation type：Oral presentation (general)  

  • Minimization problem associated with ground states to combined power-type nonlinear Schrodinger equations in three space dimensions

    菊池弘明

    「応 用 解 析 」 研 究 会  

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    Event date： 2019.6.22

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：早稲田大学  

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions International conference

    Hiroaki Kikuchi

    CAIMS-SCMAI Annual Meeting 

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    Event date： 2019.6.10

    Language：English   Presentation type：Oral presentation (general)  

  • Ground states to combined power-type nonlinear Schrodinger equations in three space dimensions International conference

    Hiroaki Kikuchi

    Mini Workshop on Variational Problems 

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    Event date： 2019.6.7

    Language：English   Presentation type：Oral presentation (general)  

    Venue：早稲田大学  

  • Minimization problem associated with ground states to combined power-type nonlinear Schrodinger equations International conference

    Hiroaki Kikuchi

    Applied Math seminar 

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    Event date： 2019.1.15

    Language：English   Presentation type：Oral presentation (general)  

    Venue：University of Victoria (ビクトリア大)  

  • Minimization problem associated with ground states to combined power-type nonlinear Schrodinger equations International conference

    Hiroaki Kikuchi

    2018 CMS Winter Meeting 

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    Event date： 2018.12.9

    Language：English   Presentation type：Oral presentation (general)  

  • Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities International conference

    Hiroaki Kikuchi

    Applied Math seminar 

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    Event date： 2018.4.11

    Language：English   Presentation type：Oral presentation (general)  

    Venue：University of Victoria (ビクトリア大)  

  • Uniqueness of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities

    菊池弘明

    非線形問題への常微分方程式の手法によるアプローチ 

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    Event date： 2018.3.5 - 2018.3.7

    Language：Japanese   Presentation type：Oral presentation (general)  

  • Uniqueness of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities

    菊池弘明

    第15回浜松偏微分方程式研究集会 

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    Event date： 2017.12.23 - 2017.12.24

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

  • 指数型非線形項をもつ楕円型方程式の正値解の分岐ダイアグラムについて

    菊池弘明

    九州関数方程式セミナー 

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    Event date： 2017.11.17

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

  • Singular solutions and bifurcation diagrams of elliptic equations with exponential nonlinearity

    Hiroaki Kikuchi

    愛媛大学における微分方程式セミナー 

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    Event date： 2017.8.31 - 2017.9.1

    Language：Japanese   Presentation type：Oral presentation (general)  

  • Virial functional and global dynamics for a class of nonlinear Schrodinger equations International conference

    Hiroaki Kikuchi

    RIMS 調和解析学と非線形偏微分方程式 

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    Event date： 2017.7.3 - 2017.7.5

    Language：English   Presentation type：Oral presentation (invited, special)  

  • Singular solutions and bifurcation diagrams of elliptic equations with exponential nonlinearity

    菊池弘明

    第１４７回神楽坂解析セミナー 

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    Event date： 2017.4.22

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

  • Blowup and scattering problems for a class of nonlinear Schrodinger equations International conference

    Hiroaki Kikuchi

    Analytical and Numerical Advances Around Schro"dinger Equations 

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    Event date： 2012.10.22 - 2012.10.26

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Toulous  

  • Scattering and blowup problems for a class of nonlinear Schrodinger equations International conference

    Hiroaki Kikuchi

    the 4th MSJ-SI ``NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS" 

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    Event date： 2011.9.20

    Language：English   Presentation type：Oral presentation (general)  

    Venue：九州大学  

  • 非線形シュレディンガー方程式の定在波の不安定性に関連する最小化問題について

    菊池弘明

    OCAMI 楕円型方程式研究集会～定常非線形シュレディンガー方程式の定在波解の研究～ 

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    Event date： 2011.8.11

    Language：English   Presentation type：Oral presentation (general)  

    Venue：大阪市立大学  

  • Singular solutions of semilinear elliptic equations with Sobolev supercritical nonlinearity International conference

    Hiroaki Kikuchi

    Nonlinear Wave and Dispersive equations 

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    Event date： 2011.2.15

    Language：English   Presentation type：Oral presentation (general)  

    Venue：京都大学  

  • Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities

    Hiroaki Kikuchi

    Workshop on solitary waves and related topics 

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    Event date： 2010.6.7

    Language：English   Presentation type：Oral presentation (general)  

    Venue：九州大学  

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Research Projects

  • ソボレフ臨界超臨界 の非線形偏微分方程式の解析

    2020.04

    Government Agency 

  • ソボレフ超臨界の非線形偏微分方程式の解析

    2017.04 - 2020.03

    Government Agency 

  • 調和ポテンシャルを伴う非線形シュレディンガー方程式の定在波の解析

    2014.04 - 2017.03

    Government Agency 

  • Study for nonlinear partial differential equation with Sobolev critical/supercritical nonlinearity

    Grant number：20K03706 

    菊池 弘明

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    Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）

    この研究では, 主に2つの研究を取り扱う. 一つはソボレフ臨界の増大度を持つ非線形項シュレディンガー方程式の大域挙動である. これまで空間3次元の場合は, 4次元以上とは異なり, 基底状態と呼ばれる解が存在しない場合があることが判明した. 基底状態は大域挙動を調べるのに重要な役割を果たすが, 空間3次元においては大域挙動はどのようになるかを解析したい.
    もう一つは指数型の非線形項をもつ楕円型方程式である. これまで空間3次元以上については正値解の構造を調べることが出来たが, 空間2次元においては非線形性が弱く, 解析することが難しい. 本研究ではこの空間2次元の解構造を調べたい.

Travelling overseas in which it aimed at research activities

  • 2023 FY, ,Less than a month

  • 2019 FY, Canada ,Less than a month

  • 2018 FY, Canada ,More than a month