MISC - 栄 伸一郎
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Heterogeneity-induced effects for pulse dynamics in FitzHugh–Nagumo-type systems 査読あり
Chao Nien Chen, Shin Ichiro Ei, Shin Ichiro Ei, Shyuh yaur Tzeng
Physica D: Nonlinear Phenomena 2018年01月
記述言語：英語
© 2018 Elsevier B.V. Particle like structures have been observed in many fields of science. In a homogeneous medium, a stable, standing pulse is a localized wave that may arise when nonlinear and dissipative effects are in balance. In this paper, we investigate certain phenomena associated with the dynamics of pulse solutions for a FitzHugh–Nagumo reaction–diffusion model. When two pulses are located far from one another initially, their weak interaction drives the subsequent slow dynamics. Our comprehension of the standing pulse profiles allows us to quantitatively characterize their interplay; when the diffusivity of the activator is small compared to that of the inhibitor, the two pulses repel. In addition, using a center-manifold reduction to study the presence of heterogeneities in the environment, we demonstrate that the pulses will move so as to maximize the strength of activation or minimize that of inhibition. The pulse motion will also be influenced by the reaction mechanism.
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Dynamics of localized solutions for reaction-diffusion systems on two dimensional domain : Spot dynamics on curved surface (Nonlinear Partial Differential Equations, Dynamical Systems and Their Applications)
栄 伸一郎, 柳下 浩紀
数理解析研究所講究録 1881 66 - 70 2014年04月
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2次元領域におけるスポット解の運動について(2013年度年会総合講演より)
栄 伸一郎
応用数理 24 ( 1 ) 34 - 36 2014年03月
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Mathematical Analysis for Pattern Formation Problems,A Mathematical Approach to Research Problems of Science and Technology
R. Nishii, S.-I. Ei, M. Koiso, H. Ochiai, K. Okada, S. Saito, T. Shirai, Editors
Mathematics for Industry 5, Springer 2014 133 - 139 2014年
解説・総説
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A NEW TREATMENT FOR PERIODIC SOLUTIONS AND COUPLED OSCILLATORS
Shin-Ichiro Ei, Kunishige Ohgane
KYUSHU JOURNAL OF MATHEMATICS 65 ( 2 ) 197 - 217 2011年09月
記述言語：英語 出版者・発行元：KYUSHU UNIV, FAC MATHEMATICS
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 from stationary solutions on the circle. This makes the treatment of periodic solutions far easier and systematic. We also give the rigorous proofs for this method.
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Interactive dynamics of two interfaces in a reaction diffusion system (非線形発展方程式と現象の数理--RIMS研究集会報告集)
栄 伸一郎, 辻川 亨
数理解析研究所講究録 1588 118 - 123 2008年04月
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25aVII-1 周期解の位相ダイナミクスの導出法とその応用(日本数学会応用数学分科会・日本物理学会領域11 協同企画シンポジウム 結合振動子系の数理-力学系としての構造解明と応用を目指して-,領域11,統計力学,物性基礎論,応用数学,力学,流体物理)
栄 伸一郎
日本物理学会講演概要集 63 ( 1 ) 302 - 302 2008年02月
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Dynamics of front solutions in a specific reaction-diffusion system in one dimension
Shin -Ichiro Ei, Hideo Ikeda, Takeyuki Kawana
Japan Journal of Industrial and Applied Mathematics 25 ( 1 ) 117 - 147 2008年02月
記述言語：英語 出版者・発行元：Springer Science and Business Media LLC
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 proved and the ordinary differential equations describing the dynamics of such traveling front solutions are also derived explicitly. It enables us to know rigorously precise information on the dynamics of traveling front solutions. As an application of this result, the imperfection structure under small perturbations and the dynamics of traveling front solutions on heterogeneous media are discussed.
DOI： 10.1007/bf03167516
その他リンク： http://link.springer.com/article/10.1007/BF03167516/fulltext.html
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Dynamics of front solutions in a specific reaction-diffusion system in one dimension 査読あり
Shin-Ichiro Ei, Hideo Ikeda, Takeyuki Kawana
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 25 ( 1 ) 117 - 147 2008年02月
記述言語：英語 出版者・発行元：KINOKUNIYA CO LTD
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 proved and the ordinary differential equations describing the dynamics of such traveling front solutions are also derived explicitly. It enables us to know rigorously precise information on the dynamics of traveling front solutions. As an application of this result, the imperfection structure under small perturbations and the dynamics of traveling front solutions on heterogeneous media are discussed.
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Interacting spots in reaction diffusion systems 査読あり
SI Ei, M Mimura, M Nagayama
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 14 ( 1 ) 31 - 62 2006年01月
担当区分：筆頭著者 記述言語：英語 出版者・発行元：AMER INST MATHEMATICAL SCIENCES
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, such travelling spots possess reflection property. In order to do it, we derive the reduced ordinary differential equations describing the dynamics of interacting travelling spots in RD systems by using center manifold theory. This reduction enables us to prove that two very slowly travelling spots reflect before collision as if they were elastic particles.
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Dynamics of Turing Patterns for Reaction-Diffusion Systems in a Cylindrical Domain on 2D, Proceedings of Hyperbolic problems,Theory
栄 伸一郎
Numerics and Applications 2004(eds. Asakura, Aiso, Kawashima,Matsumura, Nishibata, Nishihara) 121 - 128 2006年
Yokohama Publishers<br />
解説・総説 -
A variational approach to singular perturbation problems in reaction-diffusion systems 査読あり
SI Ei, M Kuwamura, Y Morita
PHYSICA D-NONLINEAR PHENOMENA 207 ( 3-4 ) 171 - 219 2005年08月
記述言語：英語 出版者・発行元：ELSEVIER SCIENCE BV
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 dynamics of solutions with transition layers in contrast to previous works in many literatures on singular perturbation theory. (c) 2005 Elsevier B.V. All rights reserved.
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Dynamics of Turing patterns in cylindrical domains on 2D (Mathematical Analysis in Fluid and Gas Dynamics)
栄 伸一郎
数理解析研究所講究録 1425 122 - 129 2005年04月
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Dynamics of Turing patterns in cylindrical domains in 2D,流体と気体の数学解析
栄 伸一郎
数理解析研究所講究録 1425 122 - 129 2005年
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2次元帯状領域におけるパターンの運動 (反応拡散系におけるパターン形成と漸近的幾何構造の研究)
栄 伸一郎
数理解析研究所講究録 1356 108 - 115 2004年02月
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Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimensions 査読あり
SI Ei, JC Wei
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 19 ( 2 ) 181 - 226 2002年06月
記述言語：英語 出版者・発行元：SPRINGER JAPAN KK
In this paper, the Gierer-Meinhardt model systems with finite diffusion constants in the whole space R-2 is considered. We give a regorous proof on the existence and the stability of a single spike solution, and by using such informations, the repulsive dynamics of the interacting multi single-spike solutions is also shown when distances between spike solutions are sufficiently large. This clarifies some part of the mechanism of the evolutional process of localized patterns appearing in the Gierer-Meinhardt model equations.
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Dynamics of pulse-like localized solutions in reaction-diffusion systems (International Conference on Reaction-Diffusion Systems : Theory and Applications)
栄 伸一郎, Mimura M
数理解析研究所講究録 1249 9 - 17 2002年02月
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Shin-Ichiro Ei, Juncheng Wei
Japan Journal of Industrial and Applied Mathematics 19 ( 2 ) 181 - 226 2002年
記述言語：英語 出版者・発行元：Kinokuniya Co. Ltd
In this paper, the Gierer-Meinhardt model systems with finite diffusion constants in the whole space R2 is considered. We give a regorous proof on the existence and the stability of a single spike solution, and by using such informations, the repulsive dynamics of the interacting multi single-spike solutions is also shown when distances between spike solutions are sufficiently large. This clarifies some part of the mechanism of the evolutional process of localized patterns appearing in the Gierer-Meinhardt model equations.
DOI： 10.1007/BF03167453
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2(n)-splitting or edge-splitting? A manner of splitting in dissipative systems 査読あり
S Ei, Y Nishiura, K Ueda
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 18 ( 2 ) 181 - 205 2001年06月
記述言語：英語 出版者・発行元：KINOKUNIYA CO LTD
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 also by numerics that SRP can be obtained via destabilization of standing or traveling spots. SRP is a typical example of transient dynamics, and hence it is not a priori clear that what kind of mathematical framework is appropriate to describe the dynamics. A framework in this direction is proposed by Nishiurar-Ueyama [16], i.e., hierarchy structure of saddle-node points, which gives a basis for rigorous analysis. One of the interesting observation is that when there occurs self-replication, then only spots (or pulses) located at the boundary (or edge) are able to split. Internal ones do not duplicate at all. For ID-case, this means that the number of newly born pulses increases like 2k after k-th splitting, not 2(n)-splitting where all pulses split simultaneously. The main objective in this article is two-fold: One is to construct a local invariant manifold near the onset of self-replication, and derive the nonlinear ODE on it. The other is to study the manner of splitting by analysing the resulting ODE, and answer the question "2(n)-splitting or edge-splitting?" starting from a single pulse. It turns out that only the edge-splitting occurs, which seems a natural consequence from a physical point of view, because the pulses at edge are easier to access fresh chemical resources than internal ones.
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2n-Splitting or Edge-Splitting? A Manner of Splitting in Dissipative Systems
Shin-Ichiro Ei, Yasumasa Nishiura, Kei-Ichi Ueda
Japan Journal of Industrial and Applied Mathematics 18 ( 2 ) 181 - 205 2001年
記述言語：英語 出版者・発行元：Kinokuniya Co. Ltd
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 also by numerics that SRP can be obtained via destabilization of standing or traveling spots. SRP is a typical example of transient dynamics, and hence it is not a priori clear that what kind of mathematical framework is appropriate to describe the dynamics. A framework in this direction is proposed by Nishiura-Ueyama [16], i.e., hierarchy structure of saddle-node points, which gives a basis for rigorous analysis. One of the interesting observation is that when there occurs self-replication, then only spots (or pulses) located at the boundary (or edge) are able to split. Internal ones do not duplicate at all. For 1D-case, this means that the number of newly born pulses increases like 2k after k-th splitting, not 2n-splitting where all pulses split simultaneously. The main objective in this article is two-fold: One is to construct a local invariant manifold near the onset of self-replication, and derive the nonlinear ODE on it. The other is to study the manner of splitting by analysing the resulting ODE, and answer the question "2n-splitting or edge-splitting?" starting from a single pulse. It turns out that only the edge-splitting occurs, which seems a natural consequence from a physical point of view, because the pulses at edge are easier to access fresh chemical resources than internal ones.
DOI： 10.1007/BF03168570
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A three phase partition problem arising in a competition-diffusion system
SI Ei, R Ikota, M Mimura
TOHOKU MATHEMATICAL PUBLICATIONS, NO 8 55 - 63 1998年
記述言語：英語 出版者・発行元：TOHOKU UNIV
We consider a three component competition-diffusion systems under the situation where the diffusion rats are small and the inter-specific competition rates are large. In this situation, the system has three locally stable equilibria, each of which implies that only one of the competing species survive and the other two are extinct. Since the diffusion rates are small, there appear sharp interfaces which separate whole space into 3 different regions occupied by only one of the competing species. If the system is treated in R-2, three interfacial curves may meet at one point. We derive an angle condition at the triple junction point by a formal asymptotic analysis and study the dynamics of solutions in a;neighborhood of the point as well as the dynamics of interfaces.
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Dynamics of interfaces in a scalar parabolic equation with variable diffusion coefficients
Shin-Ichiro Ei, Masato Iida, Eiji Yanagida
Japan Journal of Industrial and Applied Mathematics 14 ( 1 ) 1 - 23 1997年
記述言語：英語 出版者・発行元：Kinokuniya Co. Ltd
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 hypersurfaces which move with the time scale T = ε2t according to a certain generalized mean curvature flow. It is shown that, if the initial data have an interface which is close to Γ(0), then the interface remains close to Γ(ε2t) for t ε [0,T0/ε2]. Moreover, if T0 = ∞ and Γ(T) converges to a stable stationary hypersurface as T → ∞, then the interface remains close to Γ(ε2t) for all t ≥ 0.DOI： 10.1007/BF03167306
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Dynamics of Interfaces in a Scalar Parabolic equation with Variable coefficients 査読あり
Japan J. Indust. and Appl. Math. 14 ( 1 ) 1 1997年
記述言語：英語
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Dynamics of interfaces in a scalar parabolic equation with variable diffusion coefficients
Shin-Ichiro Ei, Masato Iida, Eiji Yanagida
Japan Journal of Industrial and Applied Mathematics 14 ( 1 ) 1 - 23 1997年
記述言語：英語 出版者・発行元：Kinokuniya Co. Ltd
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 hypersurfaces which move with the time scale T = ε2t according to a certain generalized mean curvature flow. It is shown that, if the initial data have an interface which is close to Γ(0), then the interface remains close to Γ(ε2t) for t ε [0,T0/ε2]. Moreover, if T0 = ∞ and Γ(T) converges to a stable stationary hypersurface as T → ∞, then the interface remains close to Γ(ε2t) for all t ≥ 0.DOI： 10.1007/BF03167306
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Instability of stationary solutions for equations of curvature-driven motion of curves
Shin-Ichiro Ei, Eiji Yanagida
Journal of Dynamics and Differential Equations 7 ( 3 ) 423 - 435 1995年07月
記述言語：英語 出版者・発行元：Kluwer Academic Publishers-Plenum Publishers
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, instability of stationary solutions is proved through an eigenvalue analysis. © 1995 Plenum Publishing Corporation.
DOI： 10.1007/BF02219370
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Instability of stationary solutions for equations of curvature-driven motion of curves 査読あり
Shin-Ichiro Ei, Eiji Yanagida
Journal of Dynamics and Differential Equations 7 ( 3 ) 423 - 435 1995年07月
記述言語：英語 出版者・発行元：Kluwer Academic Publishers-Plenum Publishers
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, instability of stationary solutions is proved through an eigenvalue analysis. © 1995 Plenum Publishing Corporation.
DOI： 10.1007/BF02219370
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Dynamics of interfaces in competition-diffusion systems 査読あり
S. I. Ei, E. Yanagida
SIAM Journal on Applied Mathematics 54 ( 5 ) 1355 - 1373 1994年
記述言語：英語 出版者・発行元：Soc for Industrial & Applied Mathematics Publ
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 locally stable equilibria, (u,w) = (1,0) and (0,a). In this case, interfaces may appear that separate Rn into two regions occupied by u and w, respectively. In this paper, it is shown that the normal velocity of the interface is approximately given by εθ, which is equal to the propagation speed of a traveling wave solution to the above system in one dimension. When θ = 0, it is shown that the normal velocity of the interface is approximately given by -ε2(n-1)Lκ, where L>
0 is a weighted mean of 1 and D, and κ is the mean curvature of the interface. -
Equation of motion for interacting pulses
Shin-Ichiro Ei, Takao Ohta
Physical Review E 50 ( 6 ) 4672 - 4678 1994年
記述言語：英語
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, which is a typical example of a dissipative system, the front equation obtained is the same as has been obtained previously. The pulse interaction is also derived for the Kortewegde Vries equation, emphasizing the difference between the cases with and without dissipative terms. © 1994 The American Physical Society.
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Interaction of pulses in FitzHugh-Nagumo equations, Reaction-Diffusion Equations and Their Applicationsand Computational Aspects
栄 伸一郎
China-Japan Symposium (eds.T-T. Li, M. Mimura, Y. Nishiura, Q-X. Ye) pp.6-13 1994年
World Scientific<br />
解説・総説 -
Interfacial Dynamics and Patterns印象記(学術会合報告)
栄 伸一郎
応用数理 3 ( 2 ) 142 - 145 1993年06月
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Failure of oscillations in combustion model equations,Lecture Notes in Num. Appl. Anal. 12 査読あり
S.-I. Ei, Q. Fang, M. Mimura, S. Sakamoto
Nonlinear PDE-JAPAN Symposium 2 1991(eds. K. Masuda, M. Mimura and T. Nishida) 87 - 110 1993年
解説・総説<br />
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Domain-dependency ofsolutions to combustion model equations 査読あり
栄 伸一郎
Nonlinear PDEs withapplication to patterns, waves and interfaces (eds. M. Mimuraand T. Nishida) 323 - 356 1992年
KTK Scientific Publications, Tokyo<br />
解説・総説 -
EFFECT OF DOMAIN-SHAPE ON COEXISTENCE PROBLEMS IN A COMPETITION-DIFFUSION SYSTEM 査読あり
M MIMURA, SI EI, Q FANG
JOURNAL OF MATHEMATICAL BIOLOGY 29 ( 3 ) 219 - 237 1991年
記述言語：英語 出版者・発行元：SPRINGER VERLAG
We discuss a competition-diffusion system to study coexistence problems of two competing species in a homogeneous environment. In particular, by using invariant manifold theory, effects of domain-shape are considered on this problem.
DOI： 10.1007/BF00160536
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PATTERN-FORMATION IN HETEROGENEOUS REACTION DIFFUSION ADVECTION SYSTEMS WITH AN APPLICATION TO POPULATION-DYNAMICS 査読あり
SI EI, M MIMURA
SIAM JOURNAL ON MATHEMATICAL ANALYSIS 21 ( 2 ) 346 - 361 1990年03月