Stable discontinuous stationary solutions to,reaction-diffusion-ODE systems
Szymon Cygan; Anna Marciniak-Czochra; Grzegorz Karch and Kanako Suzuki
Communications in Partial Differential Equations, 2023年04月10日, ［査読有り］

Instability of all regular stationary solutions to,reaction-diffusion-ODE systems
Journal of Differential Equations, 2022年08月28日, ［査読有り］

Dispersive estimates for quantum walks on 1D lattice
Masaya MAEDA; Hironobu SASAKI; Etsuo SEGAWA; Akito SUZUKI; Kanako SUZUKI, Masaya MAEDA, Hironobu SASAKI, Etsuo SEGAWA, Akito SUZUKI, Kanako SUZUKI, Mathematical Society of Japan (Project Euclid)
J. Math. Soc. Japan, 2022年01月27日, ［査読有り］

Criterion toward understanding non-constant solutions to p-Laplace,Neumann boundary value problem
Kanako Suzuki
Mathematical Journal of Ibaraki University, 2020年11月16日, ［査読有り］

Dynamics of solitons for nonlinear quantum walks
M. Maeda; H. Sasaki; E. Segawa; A. Suzuki; K. Suzuki, 筆頭著者,
We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically (Maeda et al 2018 Discrete Contin. Dyn. Syst.
38 3687–3703; Maeda et al 2018 Quantum Inf. Process.
17 215). It was shown that if the nonlinearity is weak, then the long time behavior of NLQWs are approximated by linear quantum walks. In this paper, we observe the linear decay of NLQWs for range of nonlinearity wider than studied in (Maeda et al 2018 Discrete Contin. Dyn. Syst.
38 3687–3703). In addition, we treat the strong nonlinear regime and show that the solitonic behavior of solutions appears. There are several kinds of soliton solutions and the dynamics becomes complicated. However, we see that there are some special cases so that we can calculate explicit form of solutions. In order to understand the nonlinear dynamics, we systematically study the collision between soliton solutions. We can find a relationship between our model and a nonlinear differential equation., IOP Publishing
Journal of Physics Communications, 2019年07月03日, ［査読有り］

Scattering and inverse scattering for nonlinear quantum walks
Masaya Maeda; Hironobu Sasaki; Etsuo Segawa; Akito Suzuki; Kanako Suzuki, We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QWs such as dispersive estimates and Strichartz estimate. Such argument is standard in the study of nonlinear Schrödinger equations and discrete nonlinear Schrödinger equations but it seems to be the first time to be applied to QWs., American Institute of Mathematical Sciences
Discrete and Continuous Dynamical Systems- Series A, 2018年07月01日, ［査読有り］

Dynamical spike solutions in a nonlocal model of pattern formation
Anna Marciniak-Czochra; Steffen Härting; Grzegorz Karch; Kanako Suzuki, Coupling a reaction-diffusion equation with ordinary differential equa-tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-Type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns., Institute of Physics Publishing
Nonlinearity, 2018年03月27日, ［査読有り］

Weak limit theorem for a nonlinear quantum walk
Masaya Maeda; Hironobu Sasaki; Etsuo Segawa; Akito Suzuki; Kanako Suzuki, 筆頭著者, 非線形量子ウォークの漸近挙動について考察した。, Springer Science and Business Media LLC
Quantum Information Processing, 2018年, ［査読有り］

Instability of turing patterns in reaction-diffusion-ODE systems
Anna Marciniak-Czochra; Grzegorz Karch; Kanako Suzuki, The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities., SPRINGER HEIDELBERG
JOURNAL OF MATHEMATICAL BIOLOGY, 2017年02月, ［査読有り］

FINITE-TIME BLOWUP OF SOLUTIONS TO SOME ACTIVATOR-INHIBITOR SYSTEMS
Grzegorz Karch; Kanako Suzuki; Jacek Zienkiewicz, We study a dynamics of solutions to a system of reaction-diffusion equations modeling a biological pattern formation. This model has activator inhibitor type nonlinearities and we show that it has solutions blowing up in a finite time. More precisely, in the case of absence of a diffusion of an activator, we show that there are solutions which blow up in a finite time at one point, only. This result holds true for the whole range of nonlinearity exponents in the considered activator-inhibitor system. Next, we consider a range of nonlinearities, where some space-homogeneous solutions blow up in a finite time and we show an analogous result for space-inhomogeneous solutions., AMER INST MATHEMATICAL SCIENCES-AIMS
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016年09月, ［査読有り］

DIFFUSION-DRIVEN BLOWUP OF NONNEGATIVE SOLUTIONS TO REACTION-DIFFUSION-ODE SYSTEMS
Anna Marciniak-Czochra; Grzegorz Karch; Kanako Suzuki; Jacek Zienkiewicz, In this paper, we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of nonnegative spatially heterogeneous solutions. Solutions of this problem preserve nonnegativity and uniform boundedness of the total mass. Moreover, for the corresponding system with two non-zero diffusion coefficients, all non negative solutions are global in time. We prove that a removal of diffusion in one of the equations leads to a finite-time blow-up of some nonnegative spatially heterogeneous solutions., KHAYYAM PUBL CO INC
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2016年07月, ［査読有り］

Concentration of least-energy solutions to a semilinear Neumann problem in thin domains
Masaya Maeda; Kanako Suzuki, We consider the following semilinear elliptic equation:
{-epsilon(2)Delta u + u - u(p) = 0, u > 0 in ohm(epsilon),
partial derivative/u partial derivative nu = 0 on partial derivative ohm(epsilon).
Here, epsilon > 0 and p > 1. Omega(epsilon) is a domain in R-2 with smooth boundary partial derivative Omega(epsilon), and nu denotes the outer unit normal to partial derivative Omega(epsilon). The domain Omega(epsilon) depends on epsilon, which shrinks to a straight line in the plane as epsilon -> 0. In this case, a least-energy solution exists for each epsilon sufficiently small, and it concentrates on a line. Moreover, the concentration line converges to the narrowest place of the domain as epsilon -> 0. (C) 2013 Elsevier Inc. All rights reserved.We consider the following semilinear elliptic equation:, ACADEMIC PRESS INC ELSEVIER SCIENCE
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014年03月, ［査読有り］

Unstable patterns in reaction-diffusion model of early carcinogenesis
Anna Marciniak-Czochra; Grzegorz Karch; Kanako Suzuki, Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. We focus on a basic model of early carcinogenesis proposed by Marciniak-Czochra and Kimmel [Comput. Math. Methods Med. 7 (2006) 189-213], [Math. Models Methods Appl. Sci. 17 (suppl.) (2007) 1693-1719], but the theory we develop applies to a wider class of pattern formation models with an autocatalytic non-diffusing component. The model exhibits diffusion-driven instability (Turing-type instability). However, we prove that all Turing-type patterns, i.e., regular stationary solutions, are unstable in the Lyapunov sense. Furthermore, we show existence of discontinuous stationary solutions, which are also unstable. (C) 2012 Elsevier Masson SAS. All rights reserved., GAUTHIER-VILLARS/EDITIONS ELSEVIER
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2013年05月, ［査読有り］

Blow-up versus global existence of solutions to aggregation equation with diffusion　　　　　　　　　　　　　　　
Grzegorz Karch; Kanako Suzuki, 筆頭著者
Applicationes Mathematicae, 2011年, ［査読有り］

On the role of basic production terms in an activator-inhibitor system modeling biological pattern formation
Kanako Suzuki; Izumi Takagi, 筆頭著者, Considered is the asymptotic behavior of solutions to a class of reaction-diffusion systems comprised of an activator and an inhibitor, which includes the system proposed by Gierer and Meinhardt as a model of biological pattern formation. By the basic production terms we mean those independent of the unknown functions. We prove that, when the basic production term for the activator is absent, some solutions with large initial data converge to the trivial state, i.e., the activator vanishes identically. Also, we demonstrate that there exist solutions which start from large initial data and converge to a small stationary solution in the case where the basic production term for the inhibitor is nontrivial and that for the activator is sufficiently small., KOBE UNIV, DEPT MATHEMATICS
Funkcialaj Ekvaciojm, 2011年, ［査読有り］

Mechanism generating spatial patterns in reaction-diffusion systems
Kanako Suzuki, GSIS SELECTED LECTURES: Exploring Collaborative Mathematics, The Editorial Committee of the Interdisciplinary Information Sciences
Interdiscip. Inform. Sci., 2011年, ［査読有り］

Spikes and diffusion waves in one-dimensional model of chemotaxis
Grzegorz Karch; Kanako Suzuki, 筆頭著者, We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity u(t) = u(xx) - (u(K' * u)) x with a given kernel K' is an element of L(1)(R). We show the existence of global-in-time nonnegative solutions and we study their large time asymptotics. Depending on K', we obtain either linear diffusion waves (i.e. the fundamental solution of the heat equation) or nonlinear diffusion waves (the fundamental solution of the viscous Burgers equation) in asymptotic expansions of solutions as t -> infinity. Moreover, for certain aggregation kernels, we show a concentration of solution on an initial time interval, which resemble a phenomenon of the spike creation, typical in chemotaxis models., IOP PUBLISHING LTD
Nonlinearity, 2010年, ［査読有り］

Collapes of patterns and effect of basic production terms in some reaction-diffusion systems　　　　　　　　　　　　　　　
Kanako Suzuki; Izumi Takagi, 筆頭著者
GAKUTO International Series, Mathematical Sciences and Applications, Current Advances in Nonlinear Analysis and Related Topics, 2010年

Behavior of solutions an activator-inhibitor system with basic production terms　　　　　　　　　　　　　　　
Kanako Suzuki; Izumi Takagi, 筆頭著者
Proceedings of Czech-Japanese Seminar in Applied Mathematics, COE Lect. Note, Kyushu Univ., 2009年, ［査読有り］

On the role of source terms in an activator-inhibitor system proposed by Gierer and Meinhardt　　　　　　　　　　　　　　　
Kanako Suzuki; Izumi Takagi, 筆頭著者
Advanced Studies in Pure Mathematics, 2007年, ［査読有り］

Determination of the limit sets of trajectories of the Gierer-Meinhardt system without diffusion　　　　　　　　　　　　　　　
Wei-Ming, Ni; Kanako Suzuki; Izumi Takagi, 筆頭著者
Advanced Studies in Pure Mathematics, 2007年, ［査読有り］

The dynamics of a kinetic activator-inhibitor system
Wei-Ming Ni; Kanako Suzuki; Izumi Takagi, 筆頭著者, In this paper we give a complete description of the entire dynamics of the kinetic system of a reaction-diffusion system proposed by A. Gierer and H. Meinhardt. In particular, the alpha-limit sets and omega-limit sets of all trajectories are determined, and it is shown that the dynamics of the system exhibits various interesting behaviors, including convergent solutions, periodic solutions, unbounded oscillating global solutions, and finite time blow-up solutions. (c) 2006 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE
J. Differential Equations, 2006年, ［査読有り］

Stability of stationary solutions to reaction-diffusion-ODE systems　　　　　　　　　　　　　　　
Turing symposium on Morphogenesis, 2024, 2024年02月09日, ［招待有り］

Instability and diffusion-driven blowup in some reaction-diffusion-ODE systems　　　　　　　　　　　　　　　
Kanako Suzuki
RIMS Workshop "Recent Trend in Ordinary Differential Equations and Their Developments", 2019年11月15日, ［招待有り］

Spatial patterns of some reaction-diffusion-ODE systems　　　　　　　　　　　　　　　
Kanako Suzuki
Modeling Biological Phenomena by Parabolic PDEs and their Analysis, 2019年06月07日, ［招待有り］

Reaction-diffusion-ODE systemの定常解の不安定性と解の挙動　　　　　　　　　　　　　　　
北陸応用数理研究会2018, 2018年02月20日, ［招待有り］

Reaction-diffusion-ODE systemの定常解の安定性とダイナミクス　　　　　　　　　　　　　　　
鈴木香奈子
RIMS共同研究（公開型）「非線形現象と反応拡散方程式」, 2017年10月27日, ［招待有り］

Unstable patterns and phenomena in some reaction- diffusion-ODE systems　　　　　　　　　　　　　　　
鈴木香奈子
RIMS共同研究（グループ型）「反応拡散方程式と非線形分散型方程式の解の挙動」, 2017年09月27日, ［招待有り］

Turing不安定性をもつReaction-diffusion-ODE 系のダイナミクスと空間パターン　　　　　　　　　　　　　　　
鈴木 香奈子
拡散成分と非拡散成分が共存する反応拡散系がつくるパターン, 2017年02月12日, ［招待有り］

Turing不安定性をもつreaction-diffusion-ODE systemの解のダイナミクス　　　　　　　　　　　　　　　
鈴木 香奈子
Turing機構に関連するパターンとダイナミクス, 2015年12月19日, ［招待有り］

Unbounded solutions to some reaction-diffusion-ODE systems modeling pattern formation　　　　　　　　　　　　　　　
Kanako Suzuki
偏微分方程式の解の形状と諸性質, 2015年11月12日, ［招待有り］

Reaction-diffusion-ODE system から考えるパターン形成－Turing不安定性とダイナミクス　　　　　　　　　　　　　　　
鈴木 香奈子
生物現象におけるパターン形成と数理, 2015年10月23日, ［招待有り］

Blowup phenomena in some reaction-diffusion-ODE systems induced by Turing instability　　　　　　　　　　　　　　　
鈴木 香奈子
パターン生成とダイナミクスの解構造の探究, 2015年06月28日, ［招待有り］

Turing instability and spatial patterns to reaction-diffusion equations modeling biological pattern formation　　　　　　　　　　　　　　　
Kanako Suzuki
Mini-Workshop on Models of Directional Movement and their Analysis, 2015年03月27日

Instability of spatial patterns and blowup phenomena in a model of pattern formation　　　　　　　　　　　　　　　
Kanako Suzuki
SNP2013 Winter, 2014年02月01日

Instability and blowup phenomena induced by diffusion in some reaction-diffusion-ODE systems　　　　　　　　　　　　　　　
Kanako Suzuki
RIMS Workshop on Mathematical Analysis of Pattern Formation Arising in Nonlinear Phenomena, 2013年11月11日

Dynamics of some reaction-diffusion-ODE systems with autocatalysis property　　　　　　　　　　　　　　　
鈴木 香奈子
第3回明治非線型数理セミナー, 2013年11月08日

Instability and blowup phenomena induced by diffusion in a model of pattern formation　　　　　　　　　　　　　　　
Kanako Suzuki
Workshop on Nonlinear Partial Differential Equations -- Japan-China Joint Project for Young Mathematicians 2013, 2013年10月25日

非拡散物質を含む反応拡散系を用いてパターン形成を考える　　　　　　　　　　　　　　　
鈴木 香奈子
2013年日本数学会秋季総合分科会 応用数学分科会, 2013年09月25日, ［招待有り］

細い領域における半線形楕円型方程式の解の集中点について　　　　　　　　　　　　　　　
鈴木 香奈子
非線形現象の数値シミュレーションと解析2013, 2013年03月08日

パターン形成を記述する反応拡散系における拡散の役割を考える　　　　　　　　　　　　　　　
鈴木 香奈子
クロスボーダーセミナー, 2013年01月14日

Behavior of solutions of some reaction-diffusion equations with autocatalysis property　　　　　　　　　　　　　　　
Kanako Suzuki
Swiss-Japanese Seminar, 2012年12月18日

Large time behavior of solutions of some reaction-diffusion equations with Turing instability　　　　　　　　　　　　　　　
Kanako Suzuki
Turing Symposium on Morphogenesis---Mathematical Approaches Sxty Years after Alan Turing---, 2012年08月30日

Stability of patterns in some reaction-diffusion systems with the diffusion-driven instability　　　　　　　　　　　　　　　
Kanako Suzuki
9th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2012年07月03日

Pattrens in systems of a single reaction-diffusion eauation coupled with ODE equations　　　　　　　　　　　　　　　
Kanako Suzuki
Second Italian-Japanese Workshop "Geometric Properties for Parabolic and Elliptic PDE's", 2011年06月21日

Asysmptotic Behaviour of solutions to one-dimensional nonlocal transport equation　　　　　　　　　　　　　　　
Kanako Suzuki
International Winter School Mathematical Analysis of Fluid Mechanics, 2011年02月08日

Patterns of the shadow system with nontrivial basic production terms　　　　　　　　　　　　　　　
Kanako Suzuki
Concentration and Related Topics on Nonlinear Problems, 2010年11月22日

Patterns in a reaction-diffusion model of early carcinogenesis　　　　　　　　　　　　　　　
Kanako Suzuki
Mini-Workshop on Modeling, Simulations and Analysis of Biological PAttern Formation, 2010年10月30日

Steady-state patterns of the shadow system with nontrivial basic production terms　　　　　　　　　　　　　　　
Kanako Suzuki
Partial Differential Equations in Mathematical Biology, 2010年09月13日

Spikes and siffusion waves in one-dimensional model of chemotaxis　　　　　　　　　　　　　　　
Kanako Suzuki
Nonlocal operators and partial differential equations, 2010年06月29日

日本数学会

日本数理生物学会

拡散－非拡散反応系における外力とダイナミクスの関連　　　　　　　　　　　　　　　
2023年04月 - 2027年03月

定常解が連続体をなす反応拡散系の非定常問題の解の挙動　　　　　　　　　　　　　　　
2023年04月 - 2026年03月

拡散誘導不安定化と非拡散過程が織り成す反応拡散系のダイナミクス探求　　　　　　　　　　　　　　　
基盤研究（C)
2018年04月 - 2024年03月

変数係数反応拡散方程式系の基礎理論――Turingの向こうに広がる光景
基盤研究（C)
東北大学
2019年04月 - 2023年03月

拡散-非拡散物質から成る反応系における相互作用とダイナミクスの関連性の探究　　　　　　　　　　　　　　　
基盤研究（C)
2014年04月 - 2017年03月

空間非一様パターンを形成する反応拡散系がもつ構造の体系的理解　　　　　　　　　　　　　　　
若手研究(B)
2011年04月 - 2013年03月