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Research

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Field of Study

○ Theory of Partial Differential Equations

Subject of Study

○ Study of Nonlinear Phenomena by Asymptotic Analysis (partial differential equations, nonlinear, asymptotic analysis, singular perturbation) (I have studied various non-linear partial differential equasions arising in modeling of nonlinear phenomena by using asymptotic analysis. Main purpose of the study is to know how the nonlinearity affects the complexity of the structure of solutions for the equations.)

Book / Paper

Book:

1. 広中 平祐 and Masayuki Ito :
数理科学事典,
Osaka Shoseki co.,ltd., Osaka, Mar. 1991.

Academic Paper (Judged Full Paper):

1. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
Quasilinear elliptic equations with slowly growing principal part and critical Orlicz-Sobolev nonlinear term,
Proceedings of the Royal Society of Edinburgh Section A Mathematics, Vol.139, 73-106, 2009.
(DOI: 10.1017/S0308210507000765)
2. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on Rn.,
Funkcialaj Ekvacioj, Vol.49, No.2, 235-267, 2006.
(DOI: 10.1619/fesi.49.235)
3. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
Limit as p → ∞ of p-Laplace eigenvalue problems and L∞-inequarity of the Poincaré type,
Differential and Integral Equations, Vol.12, No.2, 183-206, 1999.
4. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
Limit as p→∞ of p-Laplace eigenvalue problems and L∞-inequality of the Poincaré type,
Differential and Integral Equations, Vol.12, No.2, 183-206, 1999.
5. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
A bifurcation problem of some nonlinear degenerate elliptic equations,
Advances in Differential Equations, Vol.2, No.6, 895-926, 1997.
6. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
Bifurcation of radially symmetric solutions of degenerate quasilinear elliptic equations,
Differential and Integral Equations, Vol.8, No.7, 1709-1732, 1995.
7. Nobuyoshi Fukagai, Masayuki Ito and Kimiaki Narukawa :
Bifurcation of radially symmetric solutions of degenerate quasilinear elliptic equations,
Differential and Integral Equations, Vol.8, No.7, 1709-1732, 1995.
8. Masayuki Ito :
Travelling train solutions of FizHugh-Nagumo systems,
Lecture Notos in Num. Appl. Anal., Vol.9, 75-104, 1987.
9. Masayuki Ito :
特異摂動論における漸近展開法,
数学, Vol.38, No.2, 150-164, 1986.
10. Masayuki Ito :
Coexistence-equilibria for competition-diffusion systems with a small diffusion rate,
Japan Journal of Applied Mathematics, Vol.1, No.2, 299-336, 1984.
(DOI: 10.1007/BF03167062,   Elsevier: Scopus)
11. Masayuki Ito :
Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions,
Physica D: Nonlinear Phenomena, Vol.14D, No.1, 1-28, 1984.
(DOI: 10.1016/0167-2789(84)90002-2)

Academic Paper (Unrefereed Paper):

1. Nobuyoshi Fukagai, Masayuki Ito and Narukawa Kimiaki :
Variational methods in Orlicz-Sobolev spaces to quasilinear elliptic equations,
RIMS Kokyuroku, Vol.1405, 14-30, 2004.
(CiNii: 1050001202060895232)
2. Masayuki Ito :
A remark on singular perturbation method,
Hiroshima Mathematical Journal, Vol.14, 619, 1985.
3. Masayuki Ito :
On the conditional stability of non-minimal solutions of w"+exp(w)=O,
Journal of the Faculty of Science, the University of Tokyo Sec. IA, Vol.28, No.1, 81-88, 1981.
4. Masayuki Ito :
The conditional stability of stationary solutions for semilinear parabolic differential equations,
Journal of the Faculty of Science, The Univesity of Tokyo Sec. IA Math., Vol.25, 263-275, 1979.

Grants-in-Aid for Scientific Research (KAKEN Grants Database @ NII.ac.jp)

  • Free boundary problem with quasilinear elliptic equations (Project/Area Number: 22540229 )
  • Research on the structure of solutions for anisotropic quasilinear elliptic equations (Project/Area Number: 17540197 )
  • Quasilinear Elliptic Differential Equations of Critical Nonlinear Growth (Project/Area Number: 16540197 )
  • Research on quasilinear elliptic equations with rapidly growing principal parts (Project/Area Number: 14540211 )
  • Studies on Some Degenerate Quasilinear Elliptic Equations in Unbounded Domains (Project/Area Number: 11640207 )
  • Qualitative Theory of Quasilinear Degenerate Elliptic Differential Equations (Project/Area Number: 11640206 )
  • THE STUDY OF NON-LINEAR PHENOMENA BY THE ASYMPTOTIC ANALYSIS (Project/Area Number: 11640124 )
  • THE MATHEMATICAL ANALYSIS TO NON-LINEAR PHENOMENA THROUGH NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS (Project/Area Number: 09640276 )
  • 非線形現象に対する微分及び関数方程式による研究 (Project/Area Number: 08640289 )
  • 非線型微分方程式と数理物理学の研究 (Project/Area Number: 06640244 )
  • 漸近的方法による非線形備微分方程式の研究 (Project/Area Number: 04640235 )
  • 向き付け不可能な曲面の極小挿入と調和写像の研究 (Project/Area Number: 03640069 )
  • フラクタル自己相似図形の解析的研究 (Project/Area Number: 02640131 )
  • 代数系の等式と変換システムの組合せ論的研究 (Project/Area Number: 01540055 )
  • Visualization-system of spatio-temporal patterns in natural sciences (Project/Area Number: 63840001 )
  • 非線形振動と波動の数値解析的研究 (Project/Area Number: 63540172 )
  • 擬リーマン多様体の部分多様体と調和写像の研究 (Project/Area Number: 63540052 )
  • ソリトン理論にあらわれる微分方程式の研究 (Project/Area Number: 62540119 )
  • 常微分方程式系の概周期解の数値解析的研究 (Project/Area Number: 61540159 )
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