## 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

- 2020, Undergraduate Education, 1Term, Introduction to Mathematics
- 2020, Undergraduate Education, 3Term, English Seminar on Mathematics
- 2020, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
- 2020, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
- 2020, Graduate Education (Doctoral Program) , First Semester, Seminar on Nonlinear Studies
- 2020, Graduate Education (Doctoral Program) , Second Semester, Seminar on Nonlinear Studies
- 2020, Graduate Education (Master's Program) , Academic Year, Research for Academic Degree Dissertation in Mathematical and Life Sciences
- 2020, Graduate Education (Master's Program) , 1Term, Exercises in Applied Mathematics and Computational Science A
- 2020, Graduate Education (Master's Program) , 2Term, Exercises in Applied Mathematics and Computational Science A
- 2020, Graduate Education (Master's Program) , 3Term, Exercises in Applied Mathematics and Computational Science B
- 2020, Graduate Education (Master's Program) , 4Term, Exercises in Applied Mathematics and Computational Science B
- 2020, Graduate Education (Master's Program) , 4Term, Computational Mathematics B
- 2020, Graduate Education (Master's Program) , 2Term, Mathematical Analysis A
- 2020, Graduate Education (Master's Program) , 3Term, Mathematical Analysis B
- 2020, Graduate Education (Master's Program) , 2Term, Topical Seminar in Mathematical Science C
- 2020, Graduate Education (Master's Program) , 4Term, Topical Seminar in Mathematical Science D

## Research Activities

### Academic Papers

- A diffusion model for cell polarization with interactions on the membrane, Japan journal of Industrial and Applied Mathematics, 35, 261-276, 2018, January
- Turing Type Instability in a Diffusion Model with Mass Transport on the boundary, Discrete and Continuous Dynamical Systems, 40(6), 3813-3836
- Bifurcation of transition layers in reaction-diffusion systems, 1249, 90-102, 20020401
- Geometric and spectral problems arising in reaction diffusion systems, RAS Insitute of Applied Physics/Progress in nonlinear science, 1, 320-322, 20020401
- Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity, Hiroshima Mathematical Journal, 33(3), 20031201
- Spherically symmetric internal layers for activator-inhibitor systems I. Existence by aLyapunov-Schmidt reduction, Journal Differential Equations, 204(1), 56-92, 20040401
- Spherically symmetric internal layers for activator-inhibitor systems II. Stability and symmetry breaking bifurcations, Journal Differential Equations, 204(1), 93-122, 20040401
- ★, Internal layers in hight-dimensional domains, Proceedings of Royal Scoity of Edingbrugh, 128A, 350-401, 19980401
- Asymotptic expansion of interface equations for a reaction-diffusion system, Tohoku Mathematical Publications, 8, 145-158, 19980301
- 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
- Singular perturbation problems to a combustion equation in very long cylindrical domains, Studies in Advance Mathematics, 3, 75-84, 19970401
- Singular Hopf-Bifurcation in a Chemical Reaction-Diffusion System, Applied Mathematics Letters, 11, 127-131, 19980401
- Spatial homogenization and internal layers in a reaction-diffusion system, Hiroshima Mathematical Journal, 30(3), 377-402, 20001201
- Internal layers intersecting the boundary of domain in the Allen-Cahn equation, Japan Journal of Industrial and Applied Mathematics, 18(3), 697-738, 20011001
- Asymptotic expansion of interface equations for a reaction-diffusion system, Tohoku Mathematical Publications, 8, 149-158, 19980301
- Interface equations with nonlocal effects, 1178, 181-204, 20001201
- Geometric Variational Problems Arising Reaction-Diffusion Systems, 1210, 29-42, 20010501
- Dirichlet internal layers in an excitable reaction-diffusion system, Methods and Applications of Analysis, 2(2), 121-146, 19950401
- Shilnikov-Hopf bifurcations, Journal Differential Equations, 119(1), 1-23, 19950101
- Smooth linearization of vector fields near invariant manifolds, Hiroshima Mathematical Journal, 24(2), 331-355, 19940401
- Estimates on the strength of exponential dichotomies and application to integral manifolds, Journal Differential Equations, 107(2), 259-279, 19940401
- ★, Construction and stability analysis of transition layer solutions in reaction-diffusion systems, Tohoku Mathematical Journal, 42(1), 17-44, 19900401
- ★, Invariant manifolds in sigular perturbation problems for ordinary differential equations, Proceedings of Royal Society of Edinburgh, 116A(1-2), 45-78, 19900401
- Shadow systems and attractors in reaction-diffusion equations, Applicable Analysis, 32(3-4), 287-303, 19890401
- ★, Existence and stability of transition layers, Japan Journal of Applied Mathematics, 5(3), 367-405, 19880401
- 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
- FRONT MOTION IN VISCOUS CONSERVATION LAWS WITH STIFF SOURCE TERMS, ADVANCES IN DIFFERENTIAL EQUATIONS, 11(7), 721-750, JUL 2006
- 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
- 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
- Existence and stability of three-dimensional boundary-interior layers for the Allen-Cahn equation, TAIWANESE JOURNAL OF MATHEMATICS, 9(3), 331-358, SEP 2005
- TURING TYPE MECHANISMS FOR LINEAR DIFFUSION SYSTEMS UNDER NONDIAGONAL ROBIN BOUNDARY CONDITIONS, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 45(6), 3611-3628, 2013
- 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
- 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
- Infinitely many fine modes bifurcating from radially symmetric internal layers, Asymptot. Anal. 42 (2005), no. 1-2, 55–104, 42(1-2), 55-104
- 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
- ★, A diffusion model for cell polarization with interactions on the membrane, Jpn. J. Ind. Appl. Math. 35 (2018), no. 1, 261–276.
- ★, Unstable subsystems cause Turing instability, Kodai Math. J. 35 (2012), no. 2, 215–247.
- 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.
- A Lyapunov-Schmidt method for transition layers in reaction-diffusion systems, Hiroshima Math. J. 35 (2005), no. 2, 205–249.
- 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.
- Pattern dynamics in an exothermic reaction, Physica D 84 (1995) 58-71 .

### Invited Lecture, Oral Presentation, Poster Presentation

- 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

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