池畠 良Ryo Ikehata

Last Updated :2020/10/08

所属・職名
大学院人間社会科学研究科 教授
メールアドレス
ikehatarhiroshima-u.ac.jp

基本情報

学位

  • 理学博士 (東京理科大学)
  • 理学修士 (東京理科大学)

研究分野

  • 数物系科学 / 数学 / 数学解析

研究キーワード

  • 波動方程式
  • 漸近挙動、エネルギー減衰
  • 外部問題、初期値問題
  • フーリエ解析、実解析学、関数解析学

所属学会

  • 日本数学会, 1988年10月

教育活動

授業担当

  1. 2020年, 教養教育, 1ターム, 微分積分学I[1教自,1教数]
  2. 2020年, 学部専門, 2ターム, 解析学概論
  3. 2020年, 学部専門, 4ターム, 解析学概論演習
  4. 2020年, 学部専門, 4ターム, 解析学研究法II
  5. 2020年, 学部専門, 4ターム, 解析内容研究
  6. 2020年, 学部専門, セメスター(後期), 卒業論文
  7. 2020年, 学部専門, セメスター(前期), 解析教育内容研究
  8. 2020年, 学部専門, セメスター(後期), 教職実践演習(中・高)
  9. 2020年, 博士課程・博士課程後期, 1ターム, 教科教育学講究(数学教育学領域)
  10. 2020年, 博士課程・博士課程後期, 3ターム, 教科教育学講究(数学教育学領域)
  11. 2020年, 修士課程・博士課程前期, セメスター(前期), 教科教育学融合プロジェクト
  12. 2020年, 修士課程・博士課程前期, セメスター(前期), 数学教育学特別研究A
  13. 2020年, 修士課程・博士課程前期, セメスター(後期), 数学教育学特別研究A
  14. 2020年, 修士課程・博士課程前期, 2ターム, 科学・文化と学習材デザイン基礎研究(数学)a
  15. 2020年, 博士課程・博士課程後期, セメスター(前期), 特別研究
  16. 2020年, 博士課程・博士課程後期, セメスター(後期), 特別研究

研究活動

学術論文(★は代表的な論文)

  1. ★, ENERGY DECAY ESTIMATES FOR WAVE EQUATIONS WITH A FRACTIONAL DAMPING, DIFFERENTIAL AND INTEGRAL EQUATIONS, 25巻, 9-10号, pp. 939-956, 2012
  2. ★, Optimal decay rate of the energy for wave equations with critical potential, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 65巻, 1号, pp. 183-236, 201301
  3. On the existence of global solutions for some nonlinear hyperbolic equations with Neumann conditions, TRU Mathematics, 24巻, pp. 1-17, 19880401
  4. Yosida approximation and nonlinear hyperbolic equation (with N.Okazawa), Nonlinear Analysis TMA, 15巻, pp. 479-495, 19900401
  5. On solutions to some quasilinear hyperbolic equations with nonlinear inhomogeneous terms, Nonlinear Analysis TMA, 17巻, pp. 181-203, 19910401
  6. A class of second order quasilinear evolution equations, 京都大学数理解析研究所講究録, 785巻, pp. 95-111, 19920401
  7. A class of second order quasilinear evolution equations (with N.Okazawa), J. Differential Equations., 114巻, 1号, pp. 106-131, 19940401
  8. A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms, Differential and Integral Equations, 8巻, 3号, pp. 607-616, 19950401
  9. Stable and unstable sets for evolution equations of parabolic and hyperbolic type (with T.Suzuki), Hiroshima Math. J., 26巻, 3号, pp. 475-491, 19960401
  10. On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms (with T.Matsuyama), J. Math. Anal. Appl., 204巻, pp. 729-753, 19960401
  11. Energy decay for the wave equations of Kirchhoff type with linear damping terms (with T.Matsuyama), Math. Japon., 45巻, 2号, pp. 315-335, 19970401
  12. The global behavior of weak solutions to some nonlinear wave equations, Gakuto International Series, Math. Sci. Appl. Nonlinear Wavers, 10巻, pp. 163-168, 19970401
  13. Finite and Infinite Time Blowup of Solutions to Some Semilinear Parabolic Equations, 京都大学数理解析研究所講究録, 1061巻, pp. 43-50, 19980401
  14. The Palais-Smale Condition for some semilinear parabolic Equations, 京都大学数理解析研究所講究録, 1123巻, pp. 76-82, 20000401
  15. Semilinear parabolic equations involving critical Sobolev exponent : local and asymptotic behavior of solutions (with T.Suzuki), Differential and Integral Equations, 13巻, pp. 869-901, 20000401
  16. Remarks on the decay rate for the energy of the dissipative linear wave equations in exterior domains (with A.Saeki), SUT J. Math., 36巻, 2号, pp. 267-277, 20000401
  17. Remalks on the behaviour of solutions to the linear wave equations in unbounded domains (with T.Matsuyama), Proc. School Sci. Tokai University, 36巻, 1号, pp. 1-13, 20010401
  18. The Palais-Smale Condition for the energy of some semilinear parabolic equations, Hiroshima Math. J., 30巻, pp. 117-127, 20000401
  19. Global solutions to the initial-boundary value problem for the quasilinear visco-elastic wave equations with a perturbation (with T.Matsuyama and M.Nakao), Funkcial. Ekvac., 40巻, pp. 293-312, 19970401
  20. ★, Some remarks on the wave equations with nonlinear damping and source terms, Nonlinear Analysis TMA, 27巻, pp. 1165-1175, 19960401
  21. L^{2}-behaviour of solutions to the linear heat and wave equations in an exterior domain (with T.Matsuyama), Sci. Math. Japon., 55巻, pp. 33-42, 20020401
  22. Energy decay of solutions for the semilinear dissipative wave equations in an exterior domain, Funkcial. Ekvac., 44巻, pp. 487-499, 20010401
  23. Small data global existence of solutions for dissipative wave equations in an exterior domain, Funkcial. Ekvac., 45巻, pp. 259-269, 20020401
  24. Decay estimates by moments and masses of initial data for linear damped wave equations, International J. Pure Appl. Math., 5巻, pp. 77-94, 20030401
  25. A remark on a critical exponent for the semilinear dissipative wave equation in the one dimensional half space, Differential and Integral Equations, 16巻, pp. 727-736, 20030401
  26. Recent progress for dissipative wave equations in unbounded domains, Seminar Notes of Mathematical Sciences, Ibaraki University (Soga H. et al. eds.), 5巻, pp. 12-25, 20020201
  27. Recent development of a damped wave equation in unbounded domain, Seminar Notes of Mathematical Sciences, Ibaraki University (Soga H. et al. eds.), 6巻, pp. 51-58, 20030201
  28. 波動方程式の局所エネルギー減衰, 京都大学数理解析研究所講究録, 1411巻, pp. 1-14, 20050101
  29. Some remarks on the wave equation with potential type damping coefficients, International J. Pure Appl. Math., 21巻, 1号, pp. 19-24, 20050401
  30. ★, Local energy decay for linear wave equations with initial data decaying slowly near infinity (with K. Nishihara), Gakuto International Series, Math. Sci. Appl., The 5th East Asia PDE Conference, 22巻, pp. 265-275, 20050301
  31. Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity (with G. Sobukawa)., Hokkaido Mathematical Journal, 36巻, 1号, pp. 53-71, 20070401
  32. Decay estimates of solutions for the wave equations with strong damping terms in unbounded domains, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 24巻, 9号, pp. 659-670, 200106
  33. Remark on the L-2 estimates of the density for the compressible Navier-Stokes flow in R-3, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 47巻, 4号, pp. 2519-2526, 200108
  34. Critical exponents for semilinear dissipative wave equations in R-N, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 269巻, 1号, pp. 87-97, 20020501
  35. Diffusion phenomenon for linear dissipative wave equations in an exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 186巻, 2号, pp. 633-651, 20021210
  36. ★, Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 188巻, 2号, pp. 390-405, 20030301
  37. Improved decay rates for solutions to one-dimensional linear and semilinear dissipative wave equations in all space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 277巻, 2号, pp. 555-570, 20030115
  38. L-2-convergence results for linear dissipative wave equations in unbounded domains, ASYMPTOTIC ANALYSIS, 36巻, 1号, pp. 63-74, 200310
  39. Diffusion phenomenon for second order linear evolution equations, STUDIA MATHEMATICA, 158巻, 2号, pp. 153-161, 2003
  40. Critical exponent for semilinear damped wave equations in the N-dimensional half space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 288巻, 2号, pp. 803-818, 20031215
  41. Local energy decay for linear wave equations with variable coefficients, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 306巻, 1号, pp. 330-348, 20050601
  42. Local Energy Decay for Linear Wave Equations with Localized Dissipation, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 48巻, 3号, pp. 351-366, 200512
  43. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 200巻, 1号, pp. 53-68, 20040601
  44. ★, Decay estimates of solutions for dissipative wave equations in R-N with lower power nonlinearities, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 56巻, 2号, pp. 365-373, 200404
  45. New decay estimates for linear damped wave equations and its application to nonlinear problem, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27巻, 8号, pp. 865-889, 20040525
  46. Local energy decay for linear wave equations with non-compactly supported initial data, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27巻, 16号, pp. 1881-1892, 20041110
  47. Two dimensional exterior mixed problem for semilinear damped wave equations, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 301巻, 2号, pp. 366-377, 20050115
  48. ★, Global existence of solutions for semilinear damped wave equations in R-N with noncompactly supported initial data, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 61巻, 7号, pp. 1189-1208, 20050615
  49. Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption, JOURNAL OF DIFFERENTIAL EQUATIONS, 226巻, 1号, pp. 1-29, 20060701
  50. Global existence of solutions for 2-D semilinear wave equations with dissipation localized near infinity in an exterior domain, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 29巻, 4号, pp. 479-496, 20060310
  51. Decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 67巻, 2号, pp. 398-429, 20070715
  52. Global existence of weak solutions for two-dimensional semilinear wave equations with strong damping in an exterior domain, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 68巻, 1号, pp. 154-169, 20080101
  53. Total energy decay for semilinear wave equations with a critical potential type of damping, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 69巻, 4号, pp. 1396-1401, 20080815
  54. Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 52巻, 3号, pp. 411-435, 200912
  55. Local energy decay for a class of hyperbolic equations with constant coefficients near infinity, MATHEMATISCHE NACHRICHTEN, 283巻, 5号, pp. 636-647, 201005
  56. Semi linear parabolic equation in R-N associated with critical Sobolev exponent, ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 27巻, 3号, pp. 877-900, 2010
  57. Energy decay rates of elastic waves in unbounded domain with potential type of damping, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 380巻, 1号, pp. 46-56, 20110801
  58. ★, Wave equations with strong damping in Hilbert spaces, JOURNAL OF DIFFERENTIAL EQUATIONS, 254巻, 8号, pp. 3352-3368, 20130415
  59. Sharp decay rates for wave equations with a fractional damping via new method in the Fourier space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 408巻, 1号, pp. 247-255, 20131201
  60. NEW DECAY RATES FOR A PROBLEM OF PLATE DYNAMICS WITH FRACTIONAL DAMPING, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 10巻, 3号, pp. 563-575, 201309
  61. Optimal decay rates for the system of elastic waves in R-n with structural damping, JOURNAL OF EVOLUTION EQUATIONS, 14巻, 1号, pp. 197-210, 201403
  62. ★, Asymptotic profiles for wave equations with strong damping, JOURNAL OF DIFFERENTIAL EQUATIONS, 257巻, 6号, pp. 2159-2177, 20140915
  63. ★, Some remarks on the asymptotic profiles of solutions for strongly damped wave equations on the 1-D half space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 421巻, 1号, pp. 905-916, 20150101
  64. Asymptotic behavior for abstract evolution differential equations of second order, JOURNAL OF DIFFERENTIAL EQUATIONS, 259巻, 10号, pp. 5017-5039, 20151115
  65. ASYMPTOTIC PROFILES FOR A STRONGLY DAMPED PLATE EQUATION WITH LOWER ORDER PERTURBATION, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 14巻, 5号, pp. 1759-1780, 201509
  66. Fast energy decay for wave equations with variable damping coefficients in the 1-D half line, Differential and Integral Equations, 29巻, 5,6号, pp. 421-440, 2016
  67. Optimal decay rates and asymptotic profile for the plate equation with structural damping, J. Math. Analysis and Applications, 440巻, pp. 529-560, 20160323
  68. ★, Asymptotic profile of solutions for wave equations with frictional and viscoelastic damping terms, Asymptotic Analysis, 98巻, 1-2号, pp. 59-77, 2016
  69. FAST ENERGY DECAY FOR WAVE EQUATIONS WITH VARIABLE DAMPING COEFFICIENTS IN THE 1-D HALF LINE, DIFFERENTIAL AND INTEGRAL EQUATIONS, 29巻, 5-6号, pp. 421-440, 2016
  70. Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 148巻, pp. 228-253, 201701
  71. REMARKS ON LARGE TIME BEHAVIOR OF THE L-2-NORM OF SOLUTIONS TO STRONGLY DAMPED WAVE EQUATIONS, DIFFERENTIAL AND INTEGRAL EQUATIONS, 30巻, 7-8号, pp. 505-520, 2017
  72. Remarks on the Decay Rate of the Energy for Damped Modified Boussinesq-Beam Equations on the 1-D Half Line, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 60巻, 2号, pp. 239-257, 201708
  73. Fast energy decay for wave equations with a localized damping in the n-D half space, Asymptotic Analysis, 103巻, 1-2号, pp. 77-94, 2017
  74. ★, Asymptotic profile of solutions for some wave equations with very strong structural damping, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 41巻, 13号, pp. 5074-5090, 20180915
  75. Asymptotic profile of solutions for strongly damped Klein-Gordon equations, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 42巻, 7号, pp. 2287-2301, 20190515
  76. Asymptotic Profiles of Solutions for Structural Damped Wave Equations, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 31巻, 1号, pp. 537-571, 201903
  77. OPTIMAL ENERGY DECAY RATES FOR SOME WAVE EQUATIONS WITH DOUBLE DAMPING TERMS, EVOLUTION EQUATIONS AND CONTROL THEORY, 8巻, 4号, pp. 825-846, 201912
  78. Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow, HOKKAIDO MATHEMATICAL JOURNAL, 48巻, 2号, pp. 357-383, 201906
  79. Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms, ASYMPTOTIC ANALYSIS, 114巻, 1-2号, pp. 19-36, 2019
  80. LARGE TIME BEHAVIOR OF GLOBAL SOLUTIONS TO NONLINEAR WAVE EQUATIONS WITH FRICTIONAL AND VISCOELASTIC DAMPING TERMS, OSAKA JOURNAL OF MATHEMATICS, 56巻, 4号, pp. 807-830, 201910
  81. Critical exponent for semi-linear wave equations with double damping terms in exterior domains, NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 26巻, 6号, 201912
  82. Some remarks on the local energy decay for wave equations in the whole space, Azerbaijan J. Mathematics, 9巻, 2号, pp. 167-182, 2019, July
  83. A note on decay rates of the local energy for wave equations with Lipschitz wavespeeds, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 483巻, 2号, 20200315

招待講演、口頭・ポスター発表等

  1. L^{2} decay of solutions for dissipative linear wave equations, 池畠 良, The fourth workshop on differential equations, 1999年, 招待, 英語
  2. Decay of solutions for the dissipative wave equations in an exterior domain., 池畠 良, Workshop on nonlinear dispersive and wave equations, 2000年, 招待, 英語
  3. Energy decay for the dissipative wave equations in an exterior domain, 池畠 良, The 1st east asia symposium on nonlinear PDE, 2000年, 招待, 英語
  4. Local energy decay for a perturbed wave equations, 池畠 良, "AIMS' 6th International Conference on Dynamical Systems, Differential equations and Applications (at Poitiers, France).", 2006年06月, 招待, 英語
  5. Decay estimates of solutions for dissipative wave equations, 池畠 良, "International Conference on Dynamics of Continuous, Discrete and Impulsive Systems (at London, Canada).", 2001年07月, 招待, 英語
  6. 波動方程式および消散的波動方程式の解の漸近挙動, 池畠 良, 日本数学会関数方程式分科会主催の研究集会「微分方程式の総合的研究」, 2005年12月, 招待, 日本語
  7. Local energy decay for some hyperbolic equations, 池畠 良, "Workshop on Partial Differential equations (at LNCC, Brazil)", 2005年08月, 招待, 英語
  8. Local energy decay for some hyperbolic equations., 池畠 良, "The 5th East Asia PDE Conference (at Osaka, Japan).", 2005年03月, 招待, 英語
  9. Global solutions for Semilinear wave equations with a dissipation localized near infinity in an exterior domain., 池畠 良, "AIMS' 6th International Conference on Dynamical Systems, Differential Equations and Applications (at Poitiers, France).", 2006年06月, 招待, 英語
  10. A New Movement of the Local Energy Decay for Linear Wave Equations, 池畠 良, "WCNA2004 (at Florida, USA)", 2004年07月, 招待, 英語
  11. History and recent trends on damped wave equations, 池畠 良, Mini-Course at Department of Mathematics, Federal University of Santa Catarina, Brazil, 2013年01月, 招待, 英語
  12. Energy decay estimates for wave equations with a fractional damping, 池畠 良, 9th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2012年07月, 招待, 英語
  13. 池畠良, 浜松偏微分方程式セミナー, 招待, 日本語, 静岡大学工学部数理科学科, 静岡大学工学部
  14. 池畠良, 九州関数方程式セミナー, 2015年12月11日, 招待, 日本語, 福岡大学セミナーハウス, その他
  15. Fast energy decay for wave equations with a localized damping in the n-D half space, Seminar on Partial Differential Equations at UFSC, Brasil, 2016年12月16日, 招待, 英語, Federal University of Santa Catarina, Department of Mathematics, Federal University of Santa Catarina, Florianopolis, Brazil, その他

外部資金

競争的資金等の採択状況

  1. 科学研究費助成事業(基盤研究(C)), 数理物理に現れる時間発展する偏微分方程式の減衰構造の解析とその応用, 2020年, 2024年
  2. 科学研究費助成事業(基盤研究(C)), 消散構造を持つある偏微分方程式の解の漸近形とその応用, 2015年, 2019年
  3. 科学研究費助成事業(基盤研究(C)), 変数係数双曲型偏微分方程式のエネルギー減衰とその周辺, 2010年, 2013年
  4. 科学研究費助成事業(基盤研究(A)), 非線形偏微分方程式に対する安定性解析, 2010年, 2014年
  5. 科学研究費助成事業(基盤研究(C)), 非有界領域上の双曲型方程式のエネルギー評価とその応用, 2007年, 2009年
  6. 科学研究費助成事業(基盤研究(C)), 発展方程式の解の挙動の研究, 2002年, 2004年
  7. 科学研究費助成事業(奨励研究(A)), 非線形発展方程式と安定非安定集合, 1998年, 1999年

社会活動

その他社会貢献活動(広大・部局主催含)

  1. 平成29年度専門研修講座, 「関数の理解を深め活用する力を育てる授業づくり」講座, 広島県立教育センター, 2017年/07月/28日, 2017年/07月/28日, 講師, 講演会, 教育関係者