Ryo Ikehata

Last Updated :2021/05/08

Affiliations, Positions
Graduate School of Humanities and Social Sciences, Professor
Web Site
E-mail
ikehatarhiroshima-u.ac.jp
Self-introduction
My research interest is to study Partial Differential Equations arising in Mathematical Physics, in particular, various topics and problems on Wave equations are strongly attracting me so much. These researches are done basing on Differential Calculus, Functional analysis, Real Analysis, Complex Analysis, Theory of Distribution, and so on. My policy to proceed such researches is just symbolized by a word "Don't flock". If you would like to check my research activity, please, have a look at my RG web site above. This site will give you more precise and meaningful information on me than this formal site. Thank you!

Basic Information

Major Professional Backgrounds

  • 1992/04/01, 1996/03/31, Tokyo National College of Technology, Lecturer
  • 1996/04/01, 1998/03/31, Hiroshima University, Faculty of School Education, Lecturer

Academic Degrees

  • Doctor of Science, Tokyo University of Science
  • Master of Science, Tokyo University of Science

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Research Keywords

  • wave equation
  • Asymptotic profile, Energy decay
  • Exterior problem, Cauchy problem
  • Fourier Analysis, Real Analysis, Functional Analysis

Affiliated Academic Societies

  • Mathematical Society of Japan, 1988/10

Educational Activity

Course in Charge

  1. 2021, Liberal Arts Education Program1, 1Term, CalculusI
  2. 2021, Undergraduate Education, 2Term, Introduction to Analysis
  3. 2021, Undergraduate Education, 4Term, Practics in Introduction to Algebra
  4. 2021, Undergraduate Education, 4Term, Research Methods in Analysis II
  5. 2021, Undergraduate Education, 4Term, Study of Instructional Materials in Analysis
  6. 2021, Undergraduate Education, Second Semester, Graduation Thesis
  7. 2021, Undergraduate Education, First Semester, Study of Instructional Materials in Analysis Education
  8. 2021, Undergraduate Education, Second Semester, Practical Seminar for the Teaching Profession
  9. 2021, Graduate Education (Doctoral Program) , 1Term, Research into Curriculum and Instruction Sciences (Specialization in Mathematics Education)
  10. 2021, Graduate Education (Doctoral Program) , 3Term, Research into Curriculum and Instruction Sciences (Specialization in Mathematics Education)
  11. 2021, Graduate Education (Master's Program) , First Semester, Special Study in Mathematics Education A
  12. 2021, Graduate Education (Master's Program) , Second Semester, Special Study in Mathematics Education A
  13. 2021, Graduate Education (Master's Program) , 2Term, Basic Course in Teaching Material Design for Science and Culture (Mathematics) a
  14. 2021, Graduate Education (Doctoral Program) , First Semester, Special Study
  15. 2021, Graduate Education (Doctoral Program) , Second Semester, Special Study

Research Activities

Academic Papers

  1. ★, Asymptotic profile and optimal decay of solutions of some wave equations with logarithmic damping, Z. Angew. Math. Physics, 71:148, 2020, August, 27
  2. ★, ENERGY DECAY ESTIMATES FOR WAVE EQUATIONS WITH A FRACTIONAL DAMPING, DIFFERENTIAL AND INTEGRAL EQUATIONS, 25(9-10), 939-956, 2012
  3. ★, Optimal decay rate of the energy for wave equations with critical potential, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 65(1), 183-236, 201301
  4. On the existence of global solutions for some nonlinear hyperbolic equations with Neumann conditions, TRU Mathematics, 24, 1-17, 19880401
  5. Yosida approximation and nonlinear hyperbolic equation (with N.Okazawa), Nonlinear Analysis TMA, 15, 479-495, 19900401
  6. On solutions to some quasilinear hyperbolic equations with nonlinear inhomogeneous terms, Nonlinear Analysis TMA, 17, 181-203, 19910401
  7. A class of second order quasilinear evolution equations, 785, 95-111, 19920401
  8. A class of second order quasilinear evolution equations (with N.Okazawa), J. Differential Equations., 114(1), 106-131, 19940401
  9. A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms, Differential and Integral Equations, 8(3), 607-616, 19950401
  10. Stable and unstable sets for evolution equations of parabolic and hyperbolic type (with T.Suzuki), Hiroshima Math. J., 26(3), 475-491, 19960401
  11. 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, 729-753, 19960401
  12. Energy decay for the wave equations of Kirchhoff type with linear damping terms (with T.Matsuyama), Math. Japon., 45(2), 315-335, 19970401
  13. The global behavior of weak solutions to some nonlinear wave equations, Gakuto International Series, Math. Sci. Appl. Nonlinear Wavers, 10, 163-168, 19970401
  14. Finite and Infinite Time Blowup of Solutions to Some Semilinear Parabolic Equations, 1061, 43-50, 19980401
  15. The Palais-Smale Condition for some semilinear parabolic Equations, 1123, 76-82, 20000401
  16. Semilinear parabolic equations involving critical Sobolev exponent : local and asymptotic behavior of solutions (with T.Suzuki), Differential and Integral Equations, 13, 869-901, 20000401
  17. Remarks on the decay rate for the energy of the dissipative linear wave equations in exterior domains (with A.Saeki), SUT J. Math., 36(2), 267-277, 20000401
  18. Remalks on the behaviour of solutions to the linear wave equations in unbounded domains (with T.Matsuyama), Proc. School Sci. Tokai University, 36(1), 1-13, 20010401
  19. The Palais-Smale Condition for the energy of some semilinear parabolic equations, Hiroshima Math. J., 30, 117-127, 20000401
  20. 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, 293-312, 19970401
  21. ★, Some remarks on the wave equations with nonlinear damping and source terms, Nonlinear Analysis TMA, 27, 1165-1175, 19960401
  22. L^{2}-behaviour of solutions to the linear heat and wave equations in an exterior domain (with T.Matsuyama), Sci. Math. Japon., 55, 33-42, 20020401
  23. Energy decay of solutions for the semilinear dissipative wave equations in an exterior domain, Funkcial. Ekvac., 44, 487-499, 20010401
  24. Small data global existence of solutions for dissipative wave equations in an exterior domain, Funkcial. Ekvac., 45, 259-269, 20020401
  25. Decay estimates by moments and masses of initial data for linear damped wave equations, International J. Pure Appl. Math., 5, 77-94, 20030401
  26. A remark on a critical exponent for the semilinear dissipative wave equation in the one dimensional half space, Differential and Integral Equations, 16, 727-736, 20030401
  27. Recent progress for dissipative wave equations in unbounded domains, Seminar Notes of Mathematical Sciences, Ibaraki University (Soga H. et al. eds.), 5, 12-25, 20020201
  28. Recent development of a damped wave equation in unbounded domain, Seminar Notes of Mathematical Sciences, Ibaraki University (Soga H. et al. eds.), 6, 51-58, 20030201
  29. Some remarks on the wave equation with potential type damping coefficients, International J. Pure Appl. Math., 21(1), 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, 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(1), 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(9), 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(4), 2519-2526, 200108
  34. Critical exponents for semilinear dissipative wave equations in R-N, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 269(1), 87-97, 20020501
  35. Diffusion phenomenon for linear dissipative wave equations in an exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 186(2), 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(2), 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(2), 555-570, 20030115
  38. L-2-convergence results for linear dissipative wave equations in unbounded domains, ASYMPTOTIC ANALYSIS, 36(1), 63-74, 200310
  39. Diffusion phenomenon for second order linear evolution equations, STUDIA MATHEMATICA, 158(2), 153-161, 2003
  40. Critical exponent for semilinear damped wave equations in the N-dimensional half space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 288(2), 803-818, 20031215
  41. Local energy decay for linear wave equations with variable coefficients, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 306(1), 330-348, 20050601
  42. Local Energy Decay for Linear Wave Equations with Localized Dissipation, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 48(3), 351-366, 200512
  43. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 200(1), 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(2), 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(8), 865-889, 20040525
  46. Local energy decay for linear wave equations with non-compactly supported initial data, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27(16), 1881-1892, 20041110
  47. Two dimensional exterior mixed problem for semilinear damped wave equations, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 301(2), 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(7), 1189-1208, 20050615
  49. Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption, JOURNAL OF DIFFERENTIAL EQUATIONS, 226(1), 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(4), 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(2), 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(1), 154-169, 20080101
  53. Total energy decay for semilinear wave equations with a critical potential type of damping, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 69(4), 1396-1401, 20080815
  54. Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 52(3), 411-435, 200912
  55. Local energy decay for a class of hyperbolic equations with constant coefficients near infinity, MATHEMATISCHE NACHRICHTEN, 283(5), 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(3), 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(1), 46-56, 20110801
  58. ★, Wave equations with strong damping in Hilbert spaces, JOURNAL OF DIFFERENTIAL EQUATIONS, 254(8), 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(1), 247-255, 20131201
  60. NEW DECAY RATES FOR A PROBLEM OF PLATE DYNAMICS WITH FRACTIONAL DAMPING, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 10(3), 563-575, 201309
  61. Optimal decay rates for the system of elastic waves in R-n with structural damping, JOURNAL OF EVOLUTION EQUATIONS, 14(1), 197-210, 201403
  62. ★, Asymptotic profiles for wave equations with strong damping, JOURNAL OF DIFFERENTIAL EQUATIONS, 257(6), 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(1), 905-916, 20150101
  64. Asymptotic behavior for abstract evolution differential equations of second order, JOURNAL OF DIFFERENTIAL EQUATIONS, 259(10), 5017-5039, 20151115
  65. ASYMPTOTIC PROFILES FOR A STRONGLY DAMPED PLATE EQUATION WITH LOWER ORDER PERTURBATION, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 14(5), 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(5,6), 421-440, 2016
  67. Optimal decay rates and asymptotic profile for the plate equation with structural damping, J. Math. Analysis and Applications, 440, 529-560, 20160323
  68. ★, Asymptotic profile of solutions for wave equations with frictional and viscoelastic damping terms, Asymptotic Analysis, 98(1-2), 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(5-6), 421-440, 2016
  70. Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 148, 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(7-8), 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(2), 239-257, 201708
  73. Fast energy decay for wave equations with a localized damping in the n-D half space, Asymptotic Analysis, 103(1-2), 77-94, 2017
  74. ★, Asymptotic profile of solutions for some wave equations with very strong structural damping, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 41(13), 5074-5090, 20180915
  75. Asymptotic profile of solutions for strongly damped Klein-Gordon equations, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 42(7), 2287-2301, 20190515
  76. Asymptotic Profiles of Solutions for Structural Damped Wave Equations, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 31(1), 537-571, 201903
  77. OPTIMAL ENERGY DECAY RATES FOR SOME WAVE EQUATIONS WITH DOUBLE DAMPING TERMS, EVOLUTION EQUATIONS AND CONTROL THEORY, 8(4), 825-846, 201912
  78. Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow, HOKKAIDO MATHEMATICAL JOURNAL, 48(2), 357-383, 201906
  79. Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms, ASYMPTOTIC ANALYSIS, 114(1-2), 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(4), 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(6), 201912
  82. Some remarks on the local energy decay for wave equations in the whole space, Azerbaijan J. Mathematics, 9(2), 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(2), 20200315
  84. A SECOND ORDER FRACTIONAL DIFFERENTIAL EQUATION UNDER EFFECTS OF A SUPER DAMPING, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 19(9), 4433-4454, 202006
  85. Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 63(1), 133-152, 202004
  86. Thresholds for low regularity solutions to wave equations with structural damping, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 494(2), 124669, 20210215
  87. Asymptotic profiles for damped plate equations with rotational inertia terms, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 17(3), 569-589, 202009
  88. A note on optimal L-2-estimates of solutions to some strongly damped sigma-evolution equations, ASYMPTOTIC ANALYSIS, 121(1), 59-74, 2020

Invited Lecture, Oral Presentation, Poster Presentation

  1. Asymptotic profiles for wave equation with strong damping., Ryo Ikehata, With Invitation, Japanese
  2. Asymptotic profiles for wave equation with strong damping., 2015/12/11, With Invitation, Japanese, other
  3. Fast energy decay for wave equations with a localized damping in the n-D half space, Ryo IKEHATA, Seminar on Partial Differential Equations at UFSC, Brasil, 2016/12/16, With Invitation, English, Federal University of Santa Catarina, Department of Mathematics, Federal University of Santa Catarina, Florianopolis, Brazil, other

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI, 2015, 2019
  2. KAKENHI, Energy decay for hyperbolic partial differential equations with variable coefficients and its related topic, 2010, 2013
  3. KAKENHI, 2010, 2014
  4. KAKENHI, Energy estimates for hyperbolic equations in unbounded domains and their applications, 2007, 2009
  5. KAKENHI, A study on asymptotic behavior of solutions for evolution equations, 2002, 2004
  6. KAKENHI, 1998, 1999