内藤 雄基YUKI NAITO

Last Updated :2024/10/01

所属・職名
広島大学　教授
メールアドレス
yunaitohiroshima-u.ac.jp
その他連絡先
広島県東広島市鏡山1-3-1 理学部A棟218号室
TEL:082-424-7339
自己紹介
非線形偏微分方程式の解の定性的性質を研究しています。多くの微分方程式は、解を具体的に求めることができないため、方程式がもつ性質を手がかりにして、様々な数学的な手法を用いて定性的な性質を考察しています。

基本情報

主な職歴

  • 1990年10月01日, 1996年10月, 広島大学, 理学部, 助手
  • 1996年11月01日, 1999年02月, 神戸大学, 工学部, 講師
  • 1999年03月01日, 2007年03月31日, 神戸大学, 工学部, 助教授
  • 2007年04月01日, 2009年03月31日, 神戸大学, 大学院工学研究科, 准教授
  • 2009年04月01日, 2020年08月31日, 愛媛大学, 大学院理工学研究科, 教授
  • 2020年09月01日, 広島大学, 大学院先進理工系科学研究科, 教授

学歴

  • 広島大学, 大学院理学研究科, 博士課程後期数学専攻, 日本, 1989年04月, 1990年09月
  • 広島大学, 大学院理学研究科, 博士課程前期数学専攻, 日本, 1987年04月, 1989年03月
  • 広島大学, 理学部, 数学科, 日本, 1983年04月, 1987年03月

学位

  • 理学修士　(広島大学)
  • 博士（理学）　(広島大学)

担当主専攻プログラム

  • 数学プログラム

研究分野

  • 数物系科学 / 数学 / 数学解析

研究キーワード

  • 非線形偏微分方程式

所属学会

  • 日本数学会
  • 日本応用数理学会

教育活動

授業担当

  1. 2024年, 学部専門, １ターム, 数学概説
  2. 2024年, 教養教育, １ターム, 教養ゼミ
  3. 2024年, 学部専門, １ターム, 先端数学
  4. 2024年, 学部専門, ３ターム, 解析学Ｃ演習
  5. 2024年, 学部専門, ３ターム, 解析学Ｄ
  6. 2024年, 学部専門, ３ターム, 解析学Ｄ演習
  7. 2024年, 学部専門, ４ターム, 解析学特殊講義
  8. 2024年, 学部専門, セメスター（前期）, 数学情報課題研究
  9. 2024年, 学部専門, セメスター（後期）, 数学情報課題研究
  10. 2024年, 修士課程・博士課程前期, 年度, 実解析・関数方程式セミナー
  11. 2024年, 修士課程・博士課程前期, ４ターム, 数理解析特論Ｃ

研究活動

学術論文（★は代表的な論文）

  1. MULTIPLICITY OF SINGULAR SOLUTIONS TO A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS, MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 90巻, pp. 97-110, 2023
  2. Singular solutions for semilinear elliptic equations with general supercritical growth, ANNALI DI MATEMATICA PURA ED APPLICATA, 202巻, 1号, pp. 341-366, 202302
    DOIを用いた論文検索結果へのリンク
  3. Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions, JOURNAL OF DIFFERENTIAL EQUATIONS, 297巻, pp. 144-174, 20211005
    DOIを用いた論文検索結果へのリンク
  4. Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations, NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 27巻, 6号, 202010
    DOIを用いた論文検索結果へのリンク
  5. Asymptotically self-similar behaviour of global solutions for semilinear heat equations with algebraically decaying initial data, Proc. Roy. Soc. Edinburgh, 150巻, pp. 789-811, 2020
    DOIを用いた論文検索結果へのリンク
  6. Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state, Nonlinear Analysis, Theory, Methods and Applications, 181巻, pp. 265-293, 20190401
    DOIを用いた論文検索結果へのリンク
  7. Singular extremal soluitons for supercritical elliptic equations in a ball, J. Differential Equations, 265巻, pp. 2842-2885, 2018
    DOIを用いた論文検索結果へのリンク
  8. Asymptotically self-similar behaviour of global solutions for semilinear heat equations with algebraically decaying initial data, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 20190101
  9. Singular extremal solutions for supercritical elliptic equations in a ball, Journal of Differential Equations, 265巻, 7号, pp. 2842-2885, 20181005
  10. SEPARATION STRUCTURE OF RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38巻, 9号, pp. 4537-4554, 201809
    DOIを用いた論文検索結果へのリンク
  11. Rectifiable and nonrectifiable solution curves of half-linear differential systems, Mathematica Slovaca, 68巻, 3号, pp. 575-590, 20180626
    DOIを用いた論文検索結果へのリンク
  12. A priori bounds for superlinear elliptic equations with semidefinite nonlinearity, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 151巻, pp. 18-40, 201703
    DOIを用いた論文検索結果へのリンク
  13. GLOBAL ATTRACTIVITY AND CONVERGENCE RATE IN THE WEIGHTED NORM FOR A SUPERCRITICAL SEMILINEAR HEAT EQUATION, DIFFERENTIAL AND INTEGRAL EQUATIONS, 28巻, 7-8号, pp. 777-800, 201507
  14. A remark on self-similar solutions for a semilinear heat equation with critical Sobolev exponent, NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS, 64巻, pp. 461-468, 2015
  15. Existence and separation of positive radial solutions for semilinear elliptic equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 257巻, 7号, pp. 2430-2463, 201410
  16. Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity, Kodai Mathematical Journal, 37巻, 3号, pp. 646-667, 2014
  17. Bounded and unbounded oscillating solutions to a parabolic-elliptic system in two dimensional space, Communications on Pure and Applied Analysis, 12巻, 5号, pp. 1861-1880, 201309
  18. Fractal oscillations near the domain boundary of radially symmetric solutions of p-Laplace equations, Contemporary Mathematics, 601巻, pp. 325-343, 2013
  19. Characterization for rectifiable and nonrectifiable attractivity of nonautonomous systems of linear differential equations, International Journal of Differential Equations, 2013巻, 2013
  20. The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 253巻, 11号, pp. 3029-3060, 201212
  21. BLOW-UP BEHAVIOR OF SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM ON HIGHER DIMENSIONAL DOMAINS, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 32巻, 10号, pp. 3691-3713, 201210
  22. Classification of second-order linear differential equations and an application to singular elliptic eigenvalue problems, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 44巻, pp. 545-562, 201206
  23. Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent, ANNALI DI MATEMATICA PURA ED APPLICATA, 191巻, 1号, pp. 25-51, 201201
  24. Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent, ANNALI DI MATEMATICA PURA ED APPLICATA, 191巻, 1号, pp. 25-51, 201201
  25. OSCILLATING SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM RELATED TO A CHEMOTAXIS MODEL, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 31巻, pp. 1111-1118, 201109
  26. Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian, Mathematica Bohemica, to appear巻, pp. 175-184, 201106
  27. Self-similar blow-up for a chemotaxis system in higher dimensional domains, RIMS Kokyuroku BessatsuMathematical analysis on the self-organization and self-similarity, B15巻, pp. 87--99, 2009
  28. Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 69巻, 9号, pp. 3070-3083, 200811
  29. Self-similarity in chemotaxis systems, Colloquium Mathematicum, 111巻, 1号, pp. 11-34, 2008
  30. Self-similar solutions for a semilinear heat equation with critical Sobolev exponent, INDIANA UNIVERSITY MATHEMATICS JOURNAL, 57巻, 3号, pp. 1283-1315, 2008
  31. Positive solutions for semilinear elliptic equations with singular forcing terms, JOURNAL OF DIFFERENTIAL EQUATIONS, 235巻, 2号, pp. 439-483, 200704
  32. A variational approach to self-similar solutions for semilinear heat equations, Advanced Studies in Pure Mathematics, Asymptotic Analysis and Singuralities, 47巻, 2号, pp. 675-688, 2007
  33. Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity, JOURNAL OF DIFFERENTIAL EQUATIONS, 232巻, 1号, pp. 176-211, 200701
  34. Asymptotically self-similar solutions for the parabolic systems modelling chemotaxis, Banach Center Publ.Self-similar solutions of nonlinear PDE,, 74巻, pp. 149-160, 2006
  35. An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations, PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 136巻, 4号, pp. 807-835, 2006
  36. Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data, MATHEMATISCHE ANNALEN, 329巻, 1号, pp. 161-196, 200405
  37. On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 56巻, 6号, pp. 919-935, 200403
  38. Self-similar solutions to a nonlinear parabolic-elliptic system, Taiwanese Journal of Mathematics, 8巻, 1号, pp. 43-55, 2004
  39. Self-similar solutions to a parabolic system modeling chemotaxis, JOURNAL OF DIFFERENTIAL EQUATIONS, 184巻, 2号, pp. 386-421, 200209
  40. Symmetry results for semilinear elliptic equations in R-2, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 47巻, 6号, pp. 3661-3670, 200108
  41. Oscillation criteria for quasilinear elliptic equations, Nonlinear Analysis, Theory, Methods and Applications, 46巻, 5号, pp. 629-652, 2001
  42. Existence of self-similar solutions to a parabolic system modelling chemotaxis, JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 17巻, 3号, pp. 427-451, 200010
  43. Nonexistence results of positive solutions for semilinear elliptic equations in R-n, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 52巻, 3号, pp. 637-644, 200007
  44. Radial symmetry of self-similar solutions for semilinear heat equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 163巻, 2号, pp. 407-428, 200005
  45. Radial symmetry of positive solutions for semilinear elliptic equations in R^n, Journal of the Korean Mathematical Society, 37巻, 5号, pp. 751-761, 2000
  46. A note on the moving sphere method, PACIFIC JOURNAL OF MATHEMATICS, 189巻, 1号, pp. 107-115, 199905
  47. A note on radial symmetry of positive solutions for semilinear elliptic equations in R^n, Differential Integral Equations, 11巻, 6号, pp. 835-845, 1998
  48. Radial symmetry of positive solutionsfor semilinear elliptic equations on the unit ball in R^n, Funkcial. Ekvac., 41巻, 2号, pp. 215-234, 1998
  49. Oscillation and nonoscillation criteria for second order quasilinear differential equations, ACTA MATHEMATICA HUNGARICA, 76巻, 1-2号, pp. 81-99, 199707
  50. Nonexistence results of positive entire solutions for quasilinear elliptic inequalities, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 40巻, 2号, pp. 244-253, 199706
  51. Nonexistence results of positive entire solutions for quasilinear elliptic inequalities, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 40巻, 2号, pp. 244-253, 199706
  52. Entire solutions of the inequality div(A(|Du|)Du)≧f(u), Math. Z., 225巻, 1号, pp. 167-175, 199705
  53. Oscillation theory for semilinear elliptic equations with arbitrary nonlinearities, Funkcial. Ekvac., 40巻, 1号, pp. 41-55, 1997
  54. Radial symmetry of positive solutionsfor semilinear elliptic equations in a disc, Hiroshima Math. J., 26巻, 3号, pp. 531-545, 1996
  55. Uniqueness of positive solutions of quasilinear differential equations, Differential and Integral Equations, 8巻, 7号, pp. 1813-1822, 1995
  56. A note on the existence of nonoscillatory solutions of neutraldifferential equations, Hiroshima Math. J., 25巻, 3号, pp. 513-518, 1995
  57. Damped oscillation of solutions for some nonlinear second order ordinary differential equations, Adv. Math. Sci. Appl., 5巻, 1号, pp. 239-248, 1995
  58. EXISTENCE AND ASYMPTOTIC-BEHAVIOR OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENTIAL-EQUATIONS, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 188巻, 1号, pp. 227-244, 199411
  59. Strong oscillation and nonoscillation of quasilinear differential equations of second order, Differential Equations and Dynamical Systems, 2巻, 1号, pp. 1-10, 1994
  60. Bounded solutions with prescribed numbers of zeros for the Emden-Fowler differential equation, Hiroshima Math. J., 24巻, 1号, pp. 177-220, 1994
  61. Solutions with prescribed numbers of zeros for nonlinear second order differential equations, Funkcial. Ekvac., 37巻, 3号, pp. 505-520, 1994
  62. Radial entire solutions of a class of sublinear elliptic equations, Adv. Math. Sci. Appl., 21巻, 1号, pp. 231-243, 1993
  63. Asymptotic behavior of decaying nonoscillatory solutions of neutral differential equations, Funkcial. Ekvac., 35巻, 1号, pp. 95-110, 1992
  64. Nonoscillatory solutions of neutral differential equations, Hiroshima Math. J., 20巻, 2号, pp. 231-258, 1990