Affiliation
Faculty of Medicine, Department of Mathematics, Professor
Title
Professor
External link
Nakazawa Hideo
Degree
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博士（理学） ( 東京都立大学 )
Research Interests
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partial differential equations, spectral analysis, scattering theory
Research Areas
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Natural Science / Mathematical analysis / Mathematical analysis
Research History
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Faculty of Medicine, Nippon Medical School Department of Mathematics, Liberal Arts and Sciences Professor
2012.9
Professional Memberships
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The Mathematical Society of Japan
Committee Memberships
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Hill Publishing Group Inc. Editor-in-Chief for the journal of Applied Mathematics and Computations (JAMC)
2023.3
Committee type：Academic society
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Mathematics and Statistics reviewer
2021.9 - 2029.9
Committee type：Academic society
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Journal of Applied Mathematics and Computation editorial board as an editor
2021.6 - 2023.3
Committee type：Academic society
Papers
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Hideo Nakazawa
Current Trends in Analysis, its Applications and Computation. Trends in Mathematics. Birkhäuser, Cham. 633 - 641 2021.10
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Uniform resolvent estimates for stationary dissipative wave equations in an exterior domain and their application to the principle of limiting amplitude. Reviewed
Kiyoshi Mochizuki, Hideo Nakazawa
New trends in analysis and interdisciplinary applications, Trends Math. Res. Perspect., 2017. 521 - 527 2017
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Uniform resolvent estimates for Helmholtz equations in 2D exterior domain and their applications Invited Reviewed
Kiyoshi Mochizuki, Hideo Nakazawa
京都大学数理解析研究所講究録 1962 68 - 76 2015.8
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基礎科学から医学・医療を見る - 生存時間データ解析と比例ハザードモデル Invited Reviewed
中澤 秀夫
日本医科大学医学会雑誌 11 ( 1 ) 29 - 36 2015.2
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Uniform resolvent estimates for magnetic Schrödinger operators in a 2D exterior domain and their applications to related evolution equations Reviewed
Kiyoshi Mochizuki, Hideo Nakazawa
Publications of the Research Institute for Mathematical Sciences 51 ( 2 ) 319 - 336 2015
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基礎科学から医学・医療を見る - ロジスティック回帰 Invited Reviewed
中澤 秀夫
日本医科大学医学会雑誌 10 ( 4 ) 186 - 191 2014.10
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数学的散乱理論について(On mathematical Scattering Theory) Reviewed
中澤 秀夫
日本医科大学基礎科学紀要(The Bulletin of Liberal Arts & Sciences Nippon Medical School) ( 43 ) 1 - 18 2014.9
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書評「中村周：量子力学のスペクトル理論 (共立講座 21 世紀の数学, 26)」 Invited Reviewed
中澤 秀夫
日本数学会編集『数学』 66 ( 3 ) 315 - 320 2014.7
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Hideo Nakazawa
Bull. Lib. Arts & Sci. Nippon Med. Sch., 42 ( 42 ) 1 - 12 2013.9
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摩擦項を伴う波動方程式に関する注意 Reviewed
中澤 秀夫
Seminar Notes of Mathematical Sciences 14 64 - 73 2013.4
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SCATTERING FOR WAVE EQUATIONS WITH DISSIPATIVE TERMS IN LAYERED MEDIA Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS ( 65 ) 1 - 18 2011.5
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On wave equations with dissipation II Reviewed
Hideo Nakazawa
Rendiconti Istituto di Matematica, Trieste 42 165 - 183 2010
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Some results on spectral analysis of nonselfadjoint perturbations for Schrodinger and wave equations Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
Further progress in analysis. Proceedings of the 6th international ISAAC congress, Ankara, Turkey, August 13--18, 2007 465 - 475 2009
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On the Rank One Dissipative Operator and the Parseval Formula Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
METHODS OF SPECTRAL ANALYSIS IN MATHEMATICAL PHYSICS 186 241 - + 2009
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An aspect for spectral analysis of non-selfadjoint operators -Schrodinger and wave equations. MRIT 6th Workshop-Math-for-Industry Tutorial: Spectral theories of non-Hermitian operators and their application Invited Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
MRIT 6th Workshop-Math-for-Industry Tutorial: Spectral theories of non-Hermitian operators and their application, COE Lect. Note, Kyushu Univ. Fac. Math., Fukuoka 20 115 - 136 2009
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The Parseval formula for wave equations with dissipative term of rank one Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
SUT J. Math. 44 ( 1 ) 1 - 22 2008
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Non--selfadjoint perturbation of Schr\\"odinger and wave equations Invited Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
Advanced studies in Pure Mathematics: Asymptotic Analysis and Singularities 47 ( 1 ) 137 - 157 2007
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On wave equations with dissipations Reviewed
Nakazawa Hideo
Proceedings of the 4th International Conference "Analytical Methods of Analysis and Differntial Equations" (A.A.Kilbas, S.V.Rogosin eds.) 102 - 110 2006
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Exponential decay and spectral structure for wave equationwith some dissipations Reviewed
Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
Tokyo Journal of Mathematics 28 ( 2 ) 463 - 470 2005
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Inverse scattering problem in nuclear physics - Optical model Reviewed
H Isozaki, H Nakazawa, G Uhlmann
JOURNAL OF MATHEMATICAL PHYSICS 45 ( 7 ) 2613 - 2632 2004.7
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Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy Reviewed
M Kawashita, H Nakazawa, H Soga
NAGOYA MATHEMATICAL JOURNAL 174 115 - 126 2004.6
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The bounded operator which corresponds to a differential operator in L^2(R^N) Reviewed
Hideo Nakazawa, Go Hirasawa
Proc. Sch. Sci. Tokai Univ. 39 17 - 27 2004
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Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
Hiroshima Math. J. 34 ( 3 ) 345 - 369 2004
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Rapid decay of the total energy for dissipative wave equations. Reviewed
Fumihiko Hirosawa, Hideo Nakazawa
Tsukuba J. Math. 27 ( 2 ) 217 - 232 2003
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Non decay of the total energy for the wave equation with linear dissipation of spatial anisotropy Reviewed
Hideo Nakazawa
Seminar Notes of Mathematical Sciences, Ibaraki University 5 90 - 96 2002
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A note on a theorem of A. Saeki and R. Ikehata. Reviewed
Hideo Nakazawa
SUT. J. Math. 38 ( 1 ) 67 - 74 2002
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Energy decay of solutions to the wave equations with linear dissipation localized near infinity Reviewed
K Mochizuki, H Nakazawa
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 37 ( 3 ) 441 - 458 2001.11
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On the Gevrey wellposedness of the Cauchy problem for some non-Kowalewskian equations Reviewed
T Kinoshita, H Nakazawa
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 79 ( 3 ) 295 - 305 2000.3
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The principle of limiting absorption for the non-selfadjoint schrödinger operator with energy dependent potential Reviewed
Hideo Nakazawa
Tokyo Journal of Mathematics 23 ( 2 ) 519 - 536 2000
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Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation Reviewed
K Mochizuki, H Nakazawa
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 32 ( 3 ) 401 - 414 1996.10
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摩擦項をもつ波動方程式の解の漸近挙動 Reviewed
望月 清, 中澤 秀夫
京都大学数理解析研究所講究録 904 157 - 165 1994
Books
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RIMS 研究集会報告集 1975
中澤 秀夫（ Role： Editスペクトル・散乱理論とその周辺 Spectral and Scattering Theory and Related Topics）
京都大学数理解析研究所 2015.11
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教養の数学
石井 卓, 石村 園子, 泉 英明, 東條 晃次, 中澤 秀夫, 長崎 憲一, 橋口 秀子, 花田 孝郎, 星野 慶介, 山田 宏文, 横山 利章（ Role： Contributor第6章 積分）
学術図書出版株式会社 2006.3
Presentations
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Principle of limiting amplitude for dissipative wave equations in an magnetic field
Kiyoshi Mochizuki, Hideo Nakazawa
Spring Annual Meeting of the Japanese Mathematical Society, Functional Analysis Section 2023.3
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Principle of limiting amplitude for dissipative wave equations in an magnetic field
Hideo Nakazawa
Surugadai Partial Differential Equation Workshop 2022.12
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2 次元外部領域におけるヘルムホルツ方程式のリゾルベント評価とその応用 Invited
中澤 秀夫
広島大学 2012.6
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On the wave equation with dissipations International conference
中澤 秀夫
台湾国立大学 2012.12
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Uniform resolvent estimates for Helmholtz equation in an exterior domain and their application to scattering problems International conference
Hideo Nakazawa
Orlando, Florida, USA 2012.7
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2次元外部領域における磁場付きSchroedinger作用素に対する一様リゾルベント評価
中澤 秀夫, 望月 清
日本数学会 函数方程式論分科会 2014.3
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Uniform resolvent estimates for stationary Schrödinger equations in a two dimensional exterior domain and their applications Invited International conference
中澤 秀夫
名古屋大学 2013.3
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2次元外部領域におけるヘルムホルツ方程式の一様リゾルベント評価とその応用 Invited
中澤 秀夫
九州関数方程式セミナー 2014.6
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Uniform resolvent estimates for Helmholtz equations in 2D exterior domain and their applications Invited
中澤 秀夫
京都大学数理解析研究所 共同利用研究集会「保存則をもつ偏微分方程式に対する解の正則性・特異性の研究」 2014.5
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Sharp uniform resolvent estimate for Helmholtz and Schroedinger equations in an exterior domain in R^2 and their applications Invited International conference
中澤 秀夫
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications 2014.7
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ヘルムホルツ方程式の解の評価とその応用
中澤 秀夫
釧路偏微分方程式研究集会 2014.10
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摩擦項を伴う波動方程式の散乱問題とその周辺 Invited
中澤 秀夫
日本数学会秋季年会 函数方程式論分科会 2014.9
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摩擦項を伴う波動方程式の定常問題に対する一様リゾルベント評価とその応用 Invited
中澤 秀夫
第126回愛媛大学解析セミナー 2014.12
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摩擦項を伴う波動方程式の定常問題 Invited
中澤 秀夫
Linear and Nonlinear Waves, No. 12 2014.11
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摩擦項を伴う波動方程式の定常問題に対する解の評価とその応用
中澤 秀夫
信州大学偏微分方程式研究集会 2015.6
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Uniform resolvent estimates for stationary problem of dissipative wave equations in an exterior domain and the principle of limiting amplitude Invited International conference
中澤 秀夫
Critical Exponents and Nonlinear Evolution Equation 2015 2015.2
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摩擦項を伴う波動方程式の極限振幅の原理
中澤 秀夫
2015年夏の作用素論シンポジウム 2015.9
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Uniform resolvent estimate for stationary dissipative wave equations in an exterior domain and their application to the principle of limiting amplitude International conference
Hideo Nakazawa
10th International ISAAC Congress 2015.8
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磁場中のシュレディンガー方程式に対する一様リゾルベント評価とその応用 I & II Invited
中澤 秀夫
RIMS共同研究 2016.9
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2次元外部領域におけるシュレーディンガー作用素の一様リゾルベント評価とその応用 Invited
中澤 秀夫
第2回 解析学の耳袋 2015.10
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ヘルムホルツ方程式の解の評価
中澤秀夫
名古屋偏微分方程式研究集会 2018.10
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大きな摂動項を伴うヘルムホルツ方程式の一様リゾルベント評価とその応用
Hideo Nakazawa
Tsukuba Partial Differential Equation Workshop 2019.10 水野 将司(日本大学理工学部)・木下保(筑波大学数理物質)
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Some estimates of solutions of perturbed Helmholtz equations International conference
Hideo Nakazawa
ISAAC2019 Aveiro, Portugal 2019.7
Research Projects
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ヘルムホルツ方程式の解の評価と対応する非定常問題の解の平滑化評価に関する研究
2016.4 - 2023.3
Nippon Medical School Grant-in-Aid for Scientific Research (C)
中澤 秀夫, 門脇 光輝, 工学部, 望月 清, 首都大学東京, 理工学研究科, 客員教授, 渡邊 一雄, 理学部
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
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屈折現象を伴う波動伝播に対する空間遠方での漸近解析とその散乱理論への応用
2016.4 - 2019.3
科学研究費補助金 基盤研究（C） Grant-in-Aid for Scientific Research (C)
門脇 光輝, 中澤 秀夫, 医学部, 渡邊 一雄, 理学部, 渡邊 道之, 人文社会, 教育科学系
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid) Grant type：Competitive
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
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ある特異性を持つ波動伝播のグリーン関数の漸近挙動とその散乱理論への応用
2013.4 - 2016.3
科学研究費補助金 基盤研究（C） Grant-in-Aid for Scientific Research (C)
門脇 光輝, 中澤 秀夫, 医学部, 渡邊 一雄, 理学部, 渡邊 道之, 人文社会教育科学系, 教
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid) Grant type：Competitive
Grant amount：\4940000 （ Direct Cost: \3800000 、 Indirect Cost：\1140000 ）
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Resolvent estimates for Helmholtz equations in an exterior domain and their applications to scattering problems
Grant number：23540222 2011.4 - 2014.3
Chiba Institute of Technology/Nippon Medical School Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
中澤 秀夫, 門脇 光輝, 理工学研究科, 渡邊 一雄, 理学部
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
We studied the Helmholtz equation, which is appeared in classical physics as wave equations, and in quantum mechanics as Schr\"odinger equations. We established the uniform resolvent estimate including the case of a two-dimensional, which is important in the scattering problem, corresponding as the application. In particular, in 2-D case, we find that we can compensate the term which remain negative term using the Hardy type inequalities related to radiation conditions. As a result, we can prove the uniform resolvent estimate in 2D case, which was already proved in $N(\geqq3)$ D case.
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Research on the asymptotic form of the solutions to the Helmholtz equation and the application to mathematical scattering theory
Grant number：22540198 2010.4 - 2013.3
Ehime University Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
門脇 光輝, 中澤 秀夫, 医学部, 渡邊 一雄, 理学部, 渡邊 道之, 人文社会教育科学系, 教
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid) Grant type：Competitive
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
We studied the solutions to the Helmholtz equation with respect to elastic wave in 3-dimensional half space with free boundary.Especially, we studied the asymptotic forms of infinite direction of space. As the results, we obtained the asymptotic forms concerning P mode, R mode, SV mode (the reflected P wave component only), SH mode and SV+SV0 mode (except for the reflected P wave component), respectively. But, for the asymptotic forms concerning SH mode and SV+SV0 mode, the direction of North pole was excepted. We also obtained the results concerning scattering and inverse scattering problem for wave equations with dissipative terms, inverse problem for nonlinear Schrodinger equations and the regularity (at interface) of the solutions to a system of first order partial differential equation as the related topics.
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On a spectral theory for operators with dissipative terms
Grant number：20540187 2008.4 - 2011.3
Gakushuin University Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
渡邊 一雄, 門脇 光輝, 理工学研究科, 中澤 秀夫, 工学部
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid) Grant type：Competitive
Grant amount：\3770000 （ Direct Cost: \2900000 、 Indirect Cost：\870000 ）
Kadowaki, Nakazawa and Watanabe have studied for the properties of the wave operators with dissipative terms. In the case of the short range perturbations, we proved the existence of the wave operators. In the case of the long range perturbations, the energy of all solutions decays at infinity. The results appeared in Electric Journal of Differential Equation (April 2011). Watanabe studied the interface regularity of the solution for : the rotation system, the self-interactive system (MHD).
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Research on spectral structure of dissipative operators and super composition of dissipative systems
Grant number：19540189 2007.4 - 2010.3
Ehime University Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
門脇 光輝, 渡辺 一雄, 理学部, 中澤 秀夫, 工学部, 伊藤 宏, 理工学研究科, 望月 清, 理工学部
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid) Grant type：Competitive
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
We mainly did a mathematical research on the wave propagation problem with a weak dissipative (frictional) effect of appearing to physics and engineering. The research was done by using a characteristic frequency of the phenomenon that is called a spectrum. We obtained the following as main results. Concerning acoustic wave propagation in media of weak dissipative effect, we decided the spectral structure and the behavior of waves of the passage of time. Similar results were obtained concerning the reflection phenomenon when electron is entered into atom. We also decided the shape of waves when elastic waves of a half space (for example, seismic waves) is observed at far.
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非自己共役作用素のスペクトル構造の解明と散乱理論および逆問題に関する研究
2005.4 - 2008.3
Chiba Institute of Technology Grant-in-Aid for Young Scientists (B)
中澤 秀夫
Authorship：Principal investigator Grant type：Competitive
Grant amount：\3600000 （ Direct Cost: \3600000 ）
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Study for spectrum of dissipative operators and classification for the solutions of dissipative equations
Grant number：16540161 2004.4 - 2007.3
Ehime University Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
門脇 光輝, 定松 隆, 大学院理工学研究科, 猪狩 勝寿, 大学院理工学研究科, 伊藤 宏, 大学院理工学研究科, 渡辺 一雄, 理学部, 中澤 秀夫, 工学部
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid) Grant type：Competitive
Grant amount：\3100000 （ Direct Cost: \3100000 ）
1. One dimensional Scheodinger and wave equations with dissipative perturbation of rank one
By using scattering theory, we deal with Scheodinger equations with delta function as dissipative perturbation and wave equations with some dissipative term. Our assumptions of perturbation are special or artificial. However, to characterize the spectrum of generator (dissipative operator ) of equation these assumptions are need. Using the spectrum of generator obtained we construct Parseval formula and classify the behavior of the solutions. Concretely, initial data associated with real continuous spectrum and non-real spectrum are evolved scattering state and dissipative state, respectively. Therefore any solutions are represented as linear combination of these states
2. Spectral structure of generator of wave equations with some dissipations and exponential decay solutions
For wave equations with Coulomb type dissipative term or dissipative boundary condition at origin dissipations, we show existence of exponential decay or disappearing solutions. Especially we show that the spectrum of generator associated with wave equations with Coulomb type dissipative term consists with complex lower half-plain. However we do not characterize the relation between the spectrum and exponential or disappearing solution.
3. Eigenfunction expansion of solutions for wave equations with dissipative boundary condition on finite interval
We show that any solutions are represented by using eigenfunction for the generator of wave equations. The proof is done by using the separation of variable and usual Fourier series. However the solutions are represented in the energy space not usual LA 2-space
4. Out-going and In-coming subspaces of Lax-Phillips type and the proof for asymptotic completeness of wave operators
We give new definition of Out-going and In-coming spaces by using the idea of Lax-Phillips(1967). Using these subspaces and combining the proof of Perry(1980) we show asymptotic completeness.
Teaching Experience
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probability and statistics
2020.9Institution：Tokyo University of Science -
calculus 1&2
2020.9Institution：Tokyo University of Science -
medical statistics
2013.7Institution：Nippon Medical School -
statistics
2012.9Institution：Nippon Medical School -
mathematics(probability and statistics)
2012.9Institution：Nippon Medical School -
mathematics A
2011.4Institution：Chuo University -
linear algebra
2011.4Institution：Chuo University