Biological cybernetics 90(2) 125-132 Feb 2004 [Refereed]
Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimension
S.-I. Ei , J. Wei
Japan J. Ind. Appl. Math. 19(2) 181-226 2002 [Refereed]
2^n-splitting or Edge-splitting
S.-I. Ei, Y. Nishiura, K. Ueda
Japan J. Ind. Appl. Math. 18(2) 181-205 2001 [Refereed]
Segregating pattern problem in competition-diffusion systems
S.-I. Ei, R. Ikota, M. Mimura
Annals of Physics (280) 236-298 2000 [Refereed]
Singular perturbation problems to a combustion equation in very long cylindrical domains
M. Mimura, K. Sakamoto, S.-I. Ei
AMS/IP Studies in Advanced Math. 3 75-84 1997 [Refereed]
Pattern formation in heterogeneous reaction-diffusion- advection systems with an application to population dynamics
S.-I. Ei ,M. Mimura
SIAM J. Math. Anal. 21(346) 361 1990 [Refereed]
Phase separation in an activator-inhibitor medium
M. Mimura, S.-I. Ei, M. Kuwamura
Forma 4 65-73 1989 [Refereed]
The effect of non-local convection on reaction-diffusion equations
EI Shin-Ichiro
Hiroshima Math. J. 17 281-307 1987 [Refereed]
Transient and large time behavors of solutions to heterogeneous reaction-diffusion equations
Weng Wulin, Ei Shin-Ichiro, Ohgane Kunishige, Ogane Kunishige
Journal of Math-for-Industry (JMI) 4(0) 123-133 Oct 2012
Based on neurophysiological studies, a walking model has been proposed, which is the coupling of two oscillatory systems, i.e., a central pattern generator (CPG) and a musculoskeletal system (Body). The walking model can well reproduce human walki...
Kyushu Journal of Mathematics 65(2) 197-217 Sep 2011
We develop a systematic method for deriving the phase dynamics of perturbed periodic solutions. The method is to regard periodic solutions as slowly modulated traveling solutions on the circle. There, problems are reduced to the perturbed problems...
The dynamics of a pulse for reaction-diffusion systems in 1D is considered in the neighborhood of the bifurcation point with codimension two, at which both of saddle-node and drift bifurcations occur at the same time. It is theoretically shown tha...
Japan Journal of Industrial and Applied Mathematics 25 117-147 Jan 2008
In this paper, two component reaction-diffusion systems with a specific bistable nonlinearity are concerned. The systems have the bifurcation structure of pitch-fork type of traveling front solutions with opposite velocities, which is rigorously p...
Discrete and Continuous Dynamical Systems 14 31-62 Jan 2006
This paper is concerned with the dynamics of travelling spot solutions in two dimensions. Travelling spot solutions are constructed under the bifurcation structure with Jordan block type degeneracy. It is shown that if the velocity is very slow, s...
Shin Ichiro Ei, Masataka Kuwamura, Yoshihisa Morita
Physica D: Nonlinear Phenomena 207 171-219 Aug 2005
In this paper singular perturbation problems in reaction-diffusion systems are studied from a viewpoint of variational principle. The goal of the study is to provide an unified and transparent framework to understand existence, stability and dynam...
Reaction-dffusion systems in an infinitely long strip-like domain with finite width in 2D are treated.We construct the solution connecting different types of stationary solutions at infinity by considering the neighborhood of Turing instability.We...
Physica D: Nonlinear Phenomena 165 176-198 May 2002
It had been long believed that one-dimensional travelling pulses and the corresponding two-dimensional expanding rings and spiral waves arising in excitable reaction-diffusion systems annihilate when they closely approach one another. However, rec...
Japan Journal of Industrial and Applied Mathematics 19 181-226 Jan 2002
In this paper, the Gierer-Meinhardt model systems with finite diffusion constants in the whole space R2is considered. We give a regorous proof on the existence and the stability of a single spike solution, and by using such informations, the repul...
Journal of Dynamics and Differential Equations 14 85-137 Jan 2002
The interaction of stable pulse solutions on R1is considered when distances between pulses are sufficiently large. We construct an attractive local invariant manifold giving the dynamics of interacting pulses in a mathematically rigorous way. The ...
Shin Ichiro Ei, Yasumasa Nishiura, Yasumasa Nishiura, Kei Ichi Ueda
Japan Journal of Industrial and Applied Mathematics 18 181-205 Jan 2001
Since early 90's, much attention has been paid to dynamic dissipative patterns in laboratories, especially, self-replicating pattern (SRP) is one of the most exotic phenomena. Employing model system such as the Gray-Scott model, it is confirmed al...
The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equa...
SIAM Journal on Mathematical Analysis 29 555-595 May 1998
The dynamics of interfaces in the Allen-Cahn equation is studied. If a domain in R2 has constant width along a smooth curve, it is called a strip-like domain. We derive an equation which describes the motion of a straight interface intersecting th...
Slow dynamics of in terfaces in the Allen-Cahn eguation on a strip-like domain
Japan Journal of Industrial and Applied Mathematics 14 1-23 Jan 1997
Consider the equation ut= ε2div(D(x)∇u) + f(u;ε) in ℝn, where D(x) is a positive function of x ∈ ℝn, f is the derivative of a bistable potential, and ε > 0 is a small parameter. Let Γ(T), T ∈ [0,T0], be a one-parameter family of smooth hypersurfac...
Dynamics of Interfaces in a Scalar Parabolic equation with Variable coefficients
The dynamics of a moving hypersurface in a domain D C ℝN is studied. It is assumed that the hypersurface moves depending on its curvature, normal vector and position with the boundary that intersects ∂D with a constant contact angle. A stability c...
Journal of Dynamics and Differential Equations 7 423-435 Jul 1995
A study is made for equations of evolving curves on a two-dimensional square domain Ω. It is assumed that a curve moves depending on its curvature, normal vector, and position and is orthogonal to ∂Ω at its end points. Under some conditions, insta...
We develop a systematic method of deriving the equation of motion for interacting fronts or pulses in one dimension. The theory is applicable to both dissipative and dispersive systems. In the case of the time-dependent Ginzburg-Landau equation, w...
This paper is concerned with the dynamics of interfaces in the Lotka-Volterra competition-diffusion system ut= ε2Δu+u(1-u-cw), wt= ε2DΔw+w(a-bu-w), in Rn, where ε>0 is a small parameter and D>0 is a constant. If 0<1/c<a<b, this system has two loca...
Stability of stationary interfaces in a generalized mean curvature flow
Japan Journal of Industrial and Applied Mathematics 9 35-77 Feb 1992
We consider a bistable reaction-diffusion equation coupled with a time-dependent constrained condition {Mathematical expression} where γ, δ and ε are positive constants. This equation lies in a framework of activator-inhibitor models which arise i...
Kazutaka Ohara, Kazutaka Ohara, Kazutaka Ohara, Shin Ichiro Ei, Shin Ichiro Ei, Shin Ichiro Ei, Toshitaka Nagai, Toshitaka Nagai, Toshitaka Nagai
Hiroshima Mathematical Journal 22 365-386 Jan 1992
We are concerned with an ecological model described by a nonlinear diffusion equation with a nonlocal convection. The conditions under which stationary solutions exist are investigated. We also discuss the stability problem of stationary solutions...
Journal of Dynamics and Differential Equations 4 191-229 Jan 1992
Combustion processes are classified into three types depending upon the amount of fuel supply: two of them are the stationary states with either low or high temperatures and the other is the periodic state with relaxation oscillation type. We anal...
A size-space distribution model of biological individuals including two effects of density-dependent growth rates for size and chemotactic aggregation for space is proposed. Assuming that the spatial movement is rapid in comparison with the growth...
Two-timing Methods with Applications to Heterogeneous Reaction-Diffusion Systems
Hiroshima Mathematical Journal 14 649-678 Jan 1985
We consider initial-boundary value problems for heterogeneous reactiondiffusion equations(formula presented) and study transient and ot ox ox large time behaviors of solutions. Our method is to explicitly construct a twotiming function u(t, ϵt, x)...
Transient and Large Time Behavior of Solutions to Heterogenlous Reaction-Diffusion Eguaions
Hiroshima Mathematical J. 14 1984
Phase dynamics on the modified oscillators in Bipedal locomotion
Pulse dynamics for FitzHugh-Nagumo equation on heterogeneous media
EI Shin-Ichiro
mini-workshop on Modeling, Simulation & Analysis of Pattern Formation 27 Jul 2014
Pulse dynamics for FitzHugh-Nagumo equation on heterogeneous media
EI Shin-Ichiro
16 Jul 2014
Pulse dynamics in FitzHugh-Nagumosystems on heterogeneous media
EI Shin-Ichiro
9 Jul 2014
Dynamics of localized solutions for reaction-diffusion systems in two dimensional domains
EI Shin-Ichiro
22 Feb 2014
Motion of pulses for FitzHugh-Nagumo equation on heterogeneous media
EI Shin-Ichiro
31 Jan 2014
Dynamics of pulses for FHN on heterogeneous media
EI Shin-Ichiro
29 Nov 2013
Dynamics of Localized Solutions for Reaction-Diffusion Systems on Curved Surface
EI Shin-Ichiro
24 Oct 2013
Dynamics of Localized patterns for Reaction-Diffusion Systems on a Curved Surface
EI Shin-Ichiro
Workshop on Mathematical Modelling and Analysis in the Life Sciences 12 Jun 2013
Dynamics of Localized Solutions for Reactiondiffusion Systems on Curved Surface
EI Shin-Ichiro
IMA Special Workshop Joint US-Japan Conference for Young Researchers on Interactions among Localized Patterns in Dissipative Systems 7 Jun 2013
Renormalization-Group approach to the movement of interacting pulses
EI Shin-Ichiro
10 Sep 2012
Dynamics of localized solutions for reaction-diffusion systems on two dimensional domain,Nonlinear Partial Differential Equations,Dynamical Systems and Their Applications{in honor of Professor Hiroshi Matano on the occasion of his 60th birthday
EI Shin-Ichiro
4 Sep 2012
Dynamics of localized solutions for reaction-diffusion systems in two-dimensional domains
EI Shin-Ichiro
Turing Symposium on Morphogenesis--Mathematical Approaches Sixty Years after Alan Turing 27 Aug 2012
Infinite dimensional relaxation oscillation in a two mode randomly walking model with growth
EI Shin-Ichiro
25 Nov 2011
Infinite dimensional relaxation oscillation
EI Shin-Ichiro
LOCALIZED MULTI-DIMENSIONAL PATTERNS IN DISSIPATIVESYSTEMS: THEORY, MODELING, AND EXPERIMENTS 26 Jul 2011
Dynamics of pulses in two dimensional thin domain
EI Shin-Ichiro
The 3rd Kyushu University-POSTECH Joint Workshop- Partial Differential Equations and Fluid Dynamics 16 Jun 2011
Dynamics of pulses in two dimensional thin domain
EI Shin-Ichiro
Far-From-Equilibrium Dynamics 7 Jan 2011
Dynamics of pulses in two dimensional thin domains
EI Shin-Ichiro
29 Nov 2010
The effect of boundary conditions to the pulse dynamics
EI Shin-Ichiro
20 Feb 2010
The effect of boundary conditions to the dynamics of pulse solutions for reaction-diffusion systems
EI Shin-Ichiro
27 Dec 2009
Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems
EI Shin-Ichiro
18 Dec 2009
The effect of boundary conditions to the pulse dynamics
EI Shin-Ichiro
16 Sep 2009
The effect of boundary conditions to the dynamics of pulse solutions for reaction-diffusion systems
EI Shin-Ichiro
26 Aug 2009
The dynamics of boundary spikes for reaction-diffusion systems in 2D
EI Shin-Ichiro
2nd International conference on Reaction-diffusion systems and viscosity solutions 17 Jul 2009
The effect of boundary conditions to the pulse dynamics
EI Shin-Ichiro
Reaction-Diffusion Systems: Modeling and Analysis 2 Jun 2009
Dynamics of boundary spikes for Gierer-Meinhardt model in 2D
EI Shin-Ichiro
Verified Computation of Solutions for Partial Differential Equations and Related Topics 28 May 2009
Interaction of deformed pulses in two dimensional spaces
EI Shin-Ichiro
1 Dec 2008
Motion of a transition layer in heterogeneous environment
EI Shin-Ichiro
17 Nov 2008
The motion of a transition layer for a bistable reaction diffusion equation in one dimensional space with heterogeneous environment,Mathematical Understanding of Complex Systems arising in Biology and Medicine
EI Shin-Ichiro
CNRS Japan-France LIA ReaDiLab 27 Aug 2008
Dynamics of Pulses Constructed by Front Interaction
EI Shin-Ichiro
11 Aug 2008
The dynamics of spikes along boundaries in two dimensional space
EI Shin-Ichiro
8 Mar 2008
Boundary spikes for reaction-diffusion systems II
EI Shin-Ichiro
26 Nov 2007
The dynamics of boundary spikes for reaction-diffusion systems in space dimension 2
EI Shin-Ichiro
Mathematical modeling and analysis in biological and chemical systems 4 Sep 2007
Interface Equations for Reaction-Diffusion Systems Near Critical Point
EI Shin-Ichiro
31 May 2007
On the validity of mean curvature flow for weakly curved interfaces in reaction-diffusion systems with balanced bistable nonlinearity
EI Shin-Ichiro
19 Jan 2007
Dynamics of Pulses Constructed by Front Interaction
EI Shin-Ichiro
Internal conference on RD and Viscosity solutions 3 Jan 2007
Interface Equations for Reaction-Diffusion Systems Near Critical Point
EI Shin-Ichiro
Workshop on Reaction-Diffusion: Theory & Applications 1 Dec 2006
Front dynamics in reaction-diffusion systems
EI Shin-Ichiro
21 Oct 2006
Dynamics of front solutions in heterogeneous media
EI Shin-Ichiro
the Conference "Dynamics of nonlinear waves" 28 Apr 2006
The dynamics of boundary spikes for reaction-diffusion systems in space dimension 2
EI Shin-Ichiro
25 Jan 2006
Dynamics of front solutions in heterogeneous media
EI Shin-Ichiro
2 Dec 2005
Dynamics of front solutions of reaction-diffusion systems with bistable nonlinearity
EI Shin-Ichiro
26 Oct 2005
The motion of fronts in heterogeneous reaction-diffusion systems
EI Shin-Ichiro
13 Aug 2005
A Variational Approach to Singular Perturbation Problems
EI Shin-Ichiro
11 Aug 2005
Interacting pulses in reaction diffusion systems
EI Shin-Ichiro
7 Aug 2005
Dynamics of Turing patterns for reaction-diffusion systems in a cylindrical domain on 2D
EI Shin-Ichiro
6 Aug 2005
Dynamics of spiral solutions for reaction-diffusion systems with bistable nonlinearity
EI Shin-Ichiro
24 Jul 2005
A variational approach to singular perturbation problems
EI Shin-Ichiro
19 Nov 2004
Dynamics of pulse solutions in reaction-diffusion systems
EI Shin-Ichiro
16 Nov 2004
Dynamics of patterns in reaction-diffusion systems on two dimensions
EI Shin-Ichiro
Nonlinear PDE symposium 5 Nov 2004
A variational approach to singular perturbation problems
EI Shin-Ichiro
4 Nov 2004
Dynamics of Turing patterns for reaction-diffusion systems in a cylindrical domain on 2D
Dynamics of Turing patterns in cylindrical domains on 2D
EI Shin-Ichiro
9 Jul 2004
Dynamics of Turing patterns in cylindrical domains on 2D
EI Shin-Ichiro
NCTS 2004 Workshop on Reaction-Diffusion Equations and Related Topics 29 May 2004
Dynamics of Turing Patterns for Reaction-Diffusion Systems in a Cylindrical Domain in 2D
EI Shin-Ichiro
Mathematical Understanding of Invasion Processes in Life Sciences 16 Mar 2004
2次元帯状領域におけるTuringパターン
EI Shin-Ichiro
Hakozaki Workshop on Applied and Numerical Analysis 23 Jan 2004
The dynamics of patterns for reaction-diffusion systems in a cylindrical domain in 2D
EI Shin-Ichiro
6 Oct 2003
The dynamics of patterns for reaction-diffusion systems in a cylindrical domain in 2D
EI Shin-Ichiro
BIRS Workshops: Defects and their Dynamics and Localization Behavior in Reaction-Diffusion Systems and Applications to the Natural Sciences 13 Aug 2003
元シリンダー領域におけるパターンの運動について
EI Shin-Ichiro
Hiroshima Mathematical Analysis Seminar No.60 6 Jun 2003
A new type of the Billiard problem arising from reaction-diffusion systems
EI Shin-Ichiro
Workshop on Dynamics of Nonlinear waves 21 Jan 2003
Dynamics of patterns in reaction-diffusion systems and the related topics
EI Shin-Ichiro
25 Nov 2002
Dynamics of Pulses in Reaction-Diffusion Systems
EI Shin-Ichiro
Development of numerical nethods for dynamics of interfaces and its applications to experiments in science and Engineering II 17 Jul 2002
Pulse dynamics near a critical point in reaciton-diffusion systems
EI Shin-Ichiro
Workshop on "Singular limit analysis of reaciton-diffusion systems 10 Jul 2002
Dynamics of pulses in reaciton-diffusion systems
EI Shin-Ichiro
14 Jun 2002
Dynamics of pulse-like localized pattern in higher dimension
EI Shin-Ichiro
Traveling waves: Theory and Applications 23 Oct 2001
Pulse dynamics approach to the analysis on the self-replicating behavior
EI Shin-Ichiro
Patterns and Waves - Mathematics and NonlinearChemistry 30 Aug 2001
Invariant manifold and its application to the pulse dynamics
EI Shin-Ichiro
Workshop on "Asymptotics and Dynamics in Nonlinear Diffusive Systems 14 Jun 2001
Dynamics of pulses in reaction-diffusion systems,Singular limits of reaction-diffusion systems: Interfaces and spikes
EI Shin-Ichiro
13 Mar 2001
Minisynposium on nonlinear dynamics and dissipative systems
EI Shin-Ichiro
22 Feb 2001
Dyanamics of pulse solutions in reaction-diffusion systems
EI Shin-Ichiro
6 Dec 2000
Dynamics of localized solutions in reaction-diffusion systems
EI Shin-Ichiro
The first east Asia Symposium on Nonlinear PDE 20 Sep 2000
Dynamics of interacting pulses in reaction-diffusion systems
EI Shin-Ichiro
Organized session "Pulse dynamics in dissipative systems" 11 Aug 2000
Pulse dynamics of reaction-diffusion systems
EI Shin-Ichiro
31 May 2000
Pulse dynamics approach to self-replicating patterns
EI Shin-Ichiro
11 May 2000
The dynamics of pulses on reaction-diffusion systems II
EI Shin-Ichiro
NCTS Seminar 10 May 2000
Dynamics of pulses for reaction-diffusion systems in higher dimensional space
EI Shin-Ichiro
9 May 2000
The dynamics of pulses on reaction-diffusion systems I
EI Shin-Ichiro
NCTS Seminar 3 May 2000
Dynamics of pulses for reaction-diffusion systems in higher dimensional space
EI Shin-Ichiro
1 May 2000
The dynamics of interfaces in the scalar reaction-diffusion equations I&II
EI Shin-Ichiro
NCTS Seminar 26 Apr 2000
Dynamics of interacting pulses in reaction-diffusion systems
EI Shin-Ichiro
Equations aux Derivees Partielles Non Lineaires Frontieres libres,Interfaces et Singularites 22 Mar 2000
Pulse interaction and its application to bifurcation problems
EI Shin-Ichiro
8 Feb 2000
The dynamics of spike solutions for reaction-diffusion systems in two dimensional space
EI Shin-Ichiro
IMS Workshop on Reaction-Diffusion Systems 6 Dec 1999
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(挑戦的萌芽研究)
Project Year: 2009 - 2011 Investigator(s): Shin-ichiro EI
By considering the neighborhood of a bifurcation point, we dealt with pulses with slow velocities and investigated the effects of geometrical properties of domains on pulse motions. In fact, general methods to derive the equations of motions were ...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2004 - 2007 Investigator(s): Shin-ichiro EI
In the period of this project, we completely classified the bifurcation structures of 1 dimensional traveling front solutions and analyzed the dynamics of traveling front solutions in inhomogeneous media from the dynamical system point of view. By...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2000 - 2003 Investigator(s): Shin-ishiro EI
In this project, we considered the localized patterns in reaction-diffusion systems and tried to establish the theories to analyze the time evolutional behaviors. As the consequence, we obtained several results for the systems in 1D problems such ...
Oct 2017 Patterns and dynamics with nonlocal effect, CREST WS
Oct 2017 New mathematical approaches for understanding of biological phenomena
Oct 2017 formation problems with non-local effects
Aug 2017 One-day Workshop on Reaction-Diffusion Equations at Asahikawa 2
Aug 2016 Patterns and Waves ２０１６
Jul 2016 Joint Australia-Japan workshop on dynamical systems with applications in life sciences
Nov 2015 The 11th HU and SNU Symposium on Mathematics,Mathematical analysis and applications
Aug 2015 Mathematical Modeling and the analysis in dissipative systems
Organizers:
SHIN-ICHIRO EI*; Masaharu Nagayama (10665; 10756)
Date: August 14 Time: 13:30--15:30 Room: Room 9 ,
Date: August 14 Time: 16:00--18:00 Room: Room 9
Minisymposia in
The 8th International Congress on
Industrial and applied mathematics, August 10-14, 2015, Beijing, China.
Jul 2015 One-day Workshop on Reaction-Diffusion Equations at Asahikawa from Wednesday afternoon
July 15th to Thursday morning, July 16th, 2015
Place:
Asahikawa Medical University,
2-1-1-1, Midorigaoka-higashi, Asahikawa 078-8510, Japan,
Organizers:
Takashi Teramoto,
School of Medicine, Asahikawa Medical University,
Shin-Ichiro Ei,
Department of Mathematics, Hokkaido University
5名参加.
Sep 2011 Nonlinear dynamics in partial differential equations
