Kunimochi Sakamoto

Last Updated :2020/12/01

Affiliations, Positions
Graduate School of Integrated Sciences for Life, Professor
E-mail
knsakamotohiroshima-u.ac.jp
Self-introduction
My research interests are theory of dynamical systems and their applications (both to mathematics, an other areas of science). For systems of reaction-diffusion equations, eexistence of steady state solutions, traveling wave solutions, periodic solutions etc. and their stability are main research topics. I am aiming at using these mathematical results to some models of mathematical biology.

Basic Information

Educational Backgrounds

  • Brown University, U.S.A., 1984/09, 1988/05
  • Tohoku University, Faculty of Science, Japan, 1978/04, 1982/03

Academic Degrees

  • Ph.D. in Applied Math., Brown University
  • Master of Science, TOHOKU UNIVERSITY

Educational Activity

  • 【Bachelor Degree Program】School of Science : Mathematics
  • 【Master's Program】Graduate School of Integrated Sciences for Life : Division of Integrated Sciences for Life : Program of Mathematical and Life Sciences
  • 【Doctoral Program】Graduate School of Integrated Sciences for Life : Division of Integrated Sciences for Life : Program of Mathematical and Life Sciences

In Charge of Primary Major Programs

  • Mathematics

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Research Keywords

  • Stability
  • Open system
  • Interface

Affiliated Academic Societies

  • The Mathematical Society of Japan, 2001
  • Japanese Society of Industrial and Applied Mahtematics
  • American Mathematical Society
  • Society for Industrial and Applied Mathematics, 2019
  • The Japanese Society for Industrial and Applied Mathematics
  • The Japanese Society for Industrial and Applied Mahtematics

Educational Activity

Course in Charge

  1. 2020, Undergraduate Education, 1Term, Introduction to Mathematics
  2. 2020, Undergraduate Education, 3Term, English Seminar on Mathematics
  3. 2020, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  4. 2020, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  5. 2020, Graduate Education (Doctoral Program) , First Semester, Seminar on Nonlinear Studies
  6. 2020, Graduate Education (Doctoral Program) , Second Semester, Seminar on Nonlinear Studies
  7. 2020, Graduate Education (Master's Program) , Academic Year, Research for Academic Degree Dissertation in Mathematical and Life Sciences
  8. 2020, Graduate Education (Master's Program) , 1Term, Exercises in Applied Mathematics and Computational Science A
  9. 2020, Graduate Education (Master's Program) , 2Term, Exercises in Applied Mathematics and Computational Science A
  10. 2020, Graduate Education (Master's Program) , 3Term, Exercises in Applied Mathematics and Computational Science B
  11. 2020, Graduate Education (Master's Program) , 4Term, Exercises in Applied Mathematics and Computational Science B
  12. 2020, Graduate Education (Master's Program) , 4Term, Computational Mathematics B
  13. 2020, Graduate Education (Master's Program) , 2Term, Mathematical Analysis A
  14. 2020, Graduate Education (Master's Program) , 3Term, Mathematical Analysis B
  15. 2020, Graduate Education (Master's Program) , 2Term, Topical Seminar in Mathematical Science C
  16. 2020, Graduate Education (Master's Program) , 4Term, Topical Seminar in Mathematical Science D

Research Activities

Academic Papers

  1. A diffusion model for cell polarization with interactions on the membrane, Japan journal of Industrial and Applied Mathematics, 35, 261-276, 2018, January
  2. Turing Type Instability in a Diffusion Model with Mass Transport on the boundary, Discrete and Continuous Dynamical Systems, 40(6), 3813-3836
  3. Bifurcation of transition layers in reaction-diffusion systems, 1249, 90-102, 20020401
  4. Geometric and spectral problems arising in reaction diffusion systems, RAS Insitute of Applied Physics/Progress in nonlinear science, 1, 320-322, 20020401
  5. Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity, Hiroshima Mathematical Journal, 33(3), 20031201
  6. Spherically symmetric internal layers for activator-inhibitor systems I. Existence by aLyapunov-Schmidt reduction, Journal Differential Equations, 204(1), 56-92, 20040401
  7. Spherically symmetric internal layers for activator-inhibitor systems II. Stability and symmetry breaking bifurcations, Journal Differential Equations, 204(1), 93-122, 20040401
  8. ★, Internal layers in hight-dimensional domains, Proceedings of Royal Scoity of Edingbrugh, 128A, 350-401, 19980401
  9. Asymotptic expansion of interface equations for a reaction-diffusion system, Tohoku Mathematical Publications, 8, 145-158, 19980301
  10. Multi-dimensional transition layers for an exothermic rection-diffusion system in long cylindrical domains, Journal of Mathematical Sciences= University of Tokyo, 3, 109-179, 19960201
  11. Singular perturbation problems to a combustion equation in very long cylindrical domains, Studies in Advance Mathematics, 3, 75-84, 19970401
  12. Singular Hopf-Bifurcation in a Chemical Reaction-Diffusion System, Applied Mathematics Letters, 11, 127-131, 19980401
  13. Spatial homogenization and internal layers in a reaction-diffusion system, Hiroshima Mathematical Journal, 30(3), 377-402, 20001201
  14. Internal layers intersecting the boundary of domain in the Allen-Cahn equation, Japan Journal of Industrial and Applied Mathematics, 18(3), 697-738, 20011001
  15. Asymptotic expansion of interface equations for a reaction-diffusion system, Tohoku Mathematical Publications, 8, 149-158, 19980301
  16. Interface equations with nonlocal effects, 1178, 181-204, 20001201
  17. Geometric Variational Problems Arising Reaction-Diffusion Systems, 1210, 29-42, 20010501
  18. Dirichlet internal layers in an excitable reaction-diffusion system, Methods and Applications of Analysis, 2(2), 121-146, 19950401
  19. Shilnikov-Hopf bifurcations, Journal Differential Equations, 119(1), 1-23, 19950101
  20. Smooth linearization of vector fields near invariant manifolds, Hiroshima Mathematical Journal, 24(2), 331-355, 19940401
  21. Estimates on the strength of exponential dichotomies and application to integral manifolds, Journal Differential Equations, 107(2), 259-279, 19940401
  22. ★, Construction and stability analysis of transition layer solutions in reaction-diffusion systems, Tohoku Mathematical Journal, 42(1), 17-44, 19900401
  23. ★, Invariant manifolds in sigular perturbation problems for ordinary differential equations, Proceedings of Royal Society of Edinburgh, 116A(1-2), 45-78, 19900401
  24. Shadow systems and attractors in reaction-diffusion equations, Applicable Analysis, 32(3-4), 287-303, 19890401
  25. ★, Existence and stability of transition layers, Japan Journal of Applied Mathematics, 5(3), 367-405, 19880401
  26. Internal layers intersecting the boundary of domain in the Allen-Cahn equation, JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 18(3), 697-738, OCT 2001
  27. FRONT MOTION IN VISCOUS CONSERVATION LAWS WITH STIFF SOURCE TERMS, ADVANCES IN DIFFERENTIAL EQUATIONS, 11(7), 721-750, JUL 2006
  28. Spherically symmetric internal layers for activator-inhibitor systems I. Existence by a Lyapunov-Schmidt reduction, JOURNAL OF DIFFERENTIAL EQUATIONS, 204(1), 56-92, SEP 10 2004
  29. Spherically symmetric internal layers for activator-inhibitor systems II. Stability and symmetry breaking bifurcations, JOURNAL OF DIFFERENTIAL EQUATIONS, 204(1), 93-122, SEP 10 2004
  30. Existence and stability of three-dimensional boundary-interior layers for the Allen-Cahn equation, TAIWANESE JOURNAL OF MATHEMATICS, 9(3), 331-358, SEP 2005
  31. TURING TYPE MECHANISMS FOR LINEAR DIFFUSION SYSTEMS UNDER NONDIAGONAL ROBIN BOUNDARY CONDITIONS, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 45(6), 3611-3628, 2013
  32. DESTABILIZATION THRESHOLD CURVES FOR DIFFUSION SYSTEMS WITH EQUAL DIFFUSIVITY UNDER NON-DIAGONAL FLUX BOUNDARY CONDITIONS, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 21(2), 641-654, MAR 2016
  33. Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity, Hiroshima Math. J. 33 (2003), no. 3, 391–432., 33(3), 391-432
  34. Infinitely many fine modes bifurcating from radially symmetric internal layers, Asymptot. Anal. 42 (2005), no. 1-2, 55–104, 42(1-2), 55-104
  35. Destabilization of uniform steady states in linear diffusion systems with nonlinear boundary conditions. Nonlinear dynamics in partial differential equations, 201–207, Adv. Stud. Pure Math., 64, 64, 201-207
  36. ★, A diffusion model for cell polarization with interactions on the membrane, Jpn. J. Ind. Appl. Math. 35 (2018), no. 1, 261–276.
  37. ★, Unstable subsystems cause Turing instability, Kodai Math. J. 35 (2012), no. 2, 215–247.
  38. Travelling pulse waves non-vanishing at infinity for the derivative nonlinear Schrödinger equation, Recent progress on reaction-diffusion systems and viscosity solutions, 209–224, World Sci. Publ., Hackensack, NJ, 2009.
  39. A Lyapunov-Schmidt method for transition layers in reaction-diffusion systems, Hiroshima Math. J. 35 (2005), no. 2, 205–249.
  40. Dynamic reductions in a reaction-diffusion system—an invariant manifold approach, China-Japan Symposium on Reaction-Diffusion Equations and their Applications and Computational Aspects (Shanghai, 1994), 134–141, World Sci. Publ., River Edge, NJ, 1997.
  41. Pattern dynamics in an exothermic reaction, Physica D 84 (1995) 58-71 .

Invited Lecture, Oral Presentation, Poster Presentation

  1. A non-standard bifurcation of periodic traveling waves in the derivative nonlinear Schroedinger Equation, Kunimochi Sakamoto, The 29-th Conference on Partial Differential Equations in Kyushu, 2012/01, With Invitation, Japanese

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI, 2013, 2015
  2. KAKENHI, Reaction Diffusion Dynamics in non-homogeneous media, 2008, 2010
  3. KAKENHI, Asymptotic Analysis and Applications of Transition Layers and Interfaces, 2004, 2006
  4. KAKENHI, Singular Integral Operators and Nonlinear Problems, 2001, 2003
  5. KAKENHI, Applied mathematics of pattern formation in material sciences, 2001, 2003
  6. KAKENHI, Development of reaction-diffusion systems - Studies of singular limit methods -, 2000, 2002
  7. KAKENHI, Asymtotic Analysis of Transition Layers Intersecting the Boundary, 1999, 2000
  8. KAKENHI, Brownian Motion and Nonlinear Boundary Value Problems, 1998, 2000
  9. KAKENHI, Mathematical Studies of melting, solidification and growth phenomena in material science, 1997, 1999
  10. KAKENHI, Infinite Dimensional Transient Dynamics in Dissipative Systems, 1997, 1999
  11. KAKENHI, Internal Transition Layrs for semilinear elliptic systems and a related free boundary problem, 1997, 1998
  12. KAKENHI, Nonlinear analysis and applications, 1996, 1996
  13. KAKENHI, Mathematical Studies of singularities governed by nonlinear phenomena, 1996, 1999
  14. KAKENHI, 1995, 1995
  15. KAKENHI, 1995, 1995
  16. KAKENHI, 1994, 1994
  17. KAKENHI, Evolution equations and their applications to nonlinear problems, 1994, 1995
  18. KAKENHI, 1993, 1993
  19. KAKENHI, 2016, 2018