YUKI NAITO

Last Updated :2024/10/01

Affiliations, Positions
Professor
E-mail
yunaitohiroshima-u.ac.jp
Other Contact Details
Kagamiyama 1-3-1 Higashi-Hiroshima 739-8526, Japan
TEL : (+81)82-424-7339 FAX : (+81)
Self-introduction
My research area is the qualitative theory of nonlinear partial differential equatiotns. It is well known that exact solutions can not be derived for many differential equations. So we are interested in qualitative properties of solutions for differential equations. We will investigate the properties of solutions by employing various mathematical methods.

Basic Information

Major Professional Backgrounds

  • 1990/10/01, 1996/10, Hiroshima University, School of Science, Research Associate
  • 1996/11/01, 1999/02, Kobe University, School of Engineering, Lecturer
  • 1999/03/01, 2007/03/31, Kobe University, School of Engineering, Associate Professor
  • 2007/04/01, 2009/03/31, Kobe University, Graduate School of Engineering, Associate Professor
  • 2009/04/01, 2020/08/31, Ehime University, Professor
  • 2020/09/01, Hiroshima University, Graduate School of Advanced Science and Engineering, Professor

Educational Backgrounds

  • Hiroshima University, Graduate School of Science , Japan, 1989/04, 1990/09
  • Hiroshima University, Graduate School of Science , Japan, 1987/04, 1989/03
  • Hiroshima University, School of Science, Japan, 1983/04, 1987/03

Academic Degrees

  • Hiroshima University
  • Doctor of Science, Hiroshima University

In Charge of Primary Major Programs

  • Mathematics

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Research Keywords

  • Nonlinear Partial Differential Equations

Affiliated Academic Societies

  • The Mathematical Society of Japan
  • The Japan Society for Industrial and Applied Mathematics

Educational Activity

Course in Charge

  1. 2024, Undergraduate Education, 1Term, Introduction to Mathematics
  2. 2024, Liberal Arts Education Program1, 1Term, Introductory Seminar for First-Year Students
  3. 2024, Undergraduate Education, 1Term, Advanced Mathematics
  4. 2024, Undergraduate Education, 3Term, Exercises in Analysis C
  5. 2024, Undergraduate Education, 3Term, Analysis D
  6. 2024, Undergraduate Education, 3Term, Exercises in Analysis D
  7. 2024, Undergraduate Education, 4Term, Topics in Analysis
  8. 2024, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  9. 2024, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  10. 2024, Graduate Education (Master's Program) , Academic Year, Seminar on Real Analysis and Functional Equations
  11. 2024, Graduate Education (Master's Program) , 4Term, Topics in Mathematical Analysis C

Research Activities

Academic Papers

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