Kentaro Fujie

J-GLOBAL         Last updated: Aug 9, 2019 at 13:07
 
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Name
Kentaro Fujie
Nickname
藤江 健太郎
E-mail
fujietohoku.ac.jp
Affiliation
Tohoku University
Section
Research Alliance Center for Mathematical Sciences
Research funding number
50805398

Research Areas

 
 

Published Papers

 
Bieganowski Bartosz, Cieslak Tomasz, Fujie Kentarou, Senba Takasi
MATHEMATISCHE NACHRICHTEN   292(4) 724-732   Apr 2019   [Refereed]
Kentarou Fujie, Takasi Senba
Nonlinearity   31 1639-1672   Mar 2018   [Refereed]
© 2018 IOP Publishing Ltd & London Mathematical Society. This paper deals with time-global solutions to the parabolic system {τut= Δu - ∇ · (u∇ χ (ν)) in Ω × (0, ∞), νt= Δν - ν + u in Ω × (0,∞), under the homogeneous Neumann boundary conditions ...
Tomasz Cieślak, Kentarou Fujie
Proceedings of the American Mathematical Society   146 2529-2540   Jan 2018   [Refereed]
© 2018 Amerian Mathematial Soiety. This paper deals with the fully parabolic 1d chemotaxis system with diffusion 1/(1 + u). We prove that the above mentioned nonlinearity, despite being a natural candidate, is not critical. It means that for such ...
Fujie Kentarou, Ishida Sachiko, Ito Akio, Yokota Tomomi
Funkcialaj Ekvacioj   61(1) 37-80   Jan 2018   [Refereed]
This paper deals with a chemotaxis system modeling tumor invasion. In the previous papers [7, 8], the case of linear diffusion was studied via the Duhamel formula using the heat semigroup, whereas this method cannot be applied to the case of nonli...
Kentarou Fujie, Takasi Senba
Journal of Differential Equations      Jan 2019   [Refereed]
© 2018 Elsevier Inc. This paper deals with positive solutions of the fully parabolic system {ut=Δu−χ∇⋅(u∇v)inΩ×(0,∞),τ1vt=Δv−v+winΩ×(0,∞),τ2wt=Δw−w+uinΩ×(0,∞) under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded c...
Kentarou Fujie, Takasi Senba
Journal of Differential Equations   263 88-148   Jul 2017   [Refereed]
© 2017 Elsevier Inc. This paper deals with positive solutions of the fully parabolic system, {ut=Δu−χ∇⋅(u∇v)inΩ×(0,∞),τ1vt=Δv−v+winΩ×(0,∞),τ2wt=Δw−w+uinΩ×(0,∞), under homogeneous Neumann boundary conditions or mixed boundary conditions (no-flux an...
Tomasz Cieślak, Kentarou Fujie
   May 2017
The paper should be viewed as complement of an earlier result in [8]. In the
paper just mentioned it is shown that 1d case of a quasilinear
parabolic-elliptic Keller-Segel system is very special. Namely, unlike in
higher dimensions, there is no cr...
Kentarou Fujie, Takasi Senba
Nonlinearity   29 2417-2450   Jul 2016   [Refereed]
© 2016 IOP Publishing Ltd & London Mathematical Society Printed in the UK. This paper deals with positive radially symmetric solutions of the Neumann boundary value problem for the fully parabolic chemotaxis system, in a ball R ω R2 with general...
Kentarou Fujie, Akio Ito, Michael Winkler, Tomomi Yokota
Discrete and Continuous Dynamical Systems- Series A   36 151-169   Jan 2016   [Refereed]
This paper deals with the chemotaxis system {u<inf>t</inf> = δu -δ · (uδv), x Isin; ω, t > 0, v<inf>t</inf> = δv + wz, x ∈ ω, t > 0, w<inf>t</inf> = -wz, x ∈ ω, t > 0, z<inf>t</inf> = δz -z + u, x ∈ ω, t > 0, in a sm∞thly bounded domain ω ∪ R...
Kentarou Fujie, Takasi Senba
Discrete and Continuous Dynamical Systems - Series B   21 81-102   Jan 2016   [Refereed]
This paper is concerned with the parabolic-elliptic Keller-Segel system with signal-dependent sensitivity x(v), {ut=Δu-Δ · (uΔx(u)) in ω × (0, ∞),0=Δu-u+u in ω × (0,∞), under homogeneous Neumann boundary condition in a smoothly bounded domain ω ℝ2...
Kentarou Fujie, Michael Winkler, Tomomi Yokota
Mathematical Methods in the Applied Sciences   38 1212-1224   Jan 2015   [Refereed]
Copyright © 2014 John Wiley & Sons, Ltd. This paper deals with the parabolic-elliptic Keller-Segel system with signal-dependent chemotactic sensitivity function, ut=Δu-·(uχ(v)),x∈Ω,t>0,0=Δv-v+u,x∈Ω,t>0,under homogeneous Neumann boundary conditio...
Kentarou Fujie
Journal of Mathematical Analysis and Applications   424 675-684   Jan 2015   [Refereed]
© 2014 Elsevier Inc. This paper deals with a fully parabolic chemotaxis system ut=δu-χ∇{dot operator}(uv∇v), vt=δv-v+u with singular sensitivity χv (χ. >. 0) on a bounded domain Ω⊂Rn, n≥. 2. The main result solves the open problem of uniform-in-ti...
Kentarou Fujie, Tomomi Yokota
Applied Mathematics Letters   38 140-143   Jan 2014   [Refereed]
This paper presents global existence and boundedness of classical solutions to the fully parabolic chemotaxis systemut=Δu- ∇(uχ(v)∇v),vt=Δv-v+u with the strongly singular sensitivity function χ(v) such that 0<χ(v)≤χ0vk(χ0>0,k>1). As to the regular...
Kentarou Fujie, Michael Winkler, Tomomi Yokota
Nonlinear Analysis, Theory, Methods and Applications   109 56-71   Jan 2014   [Refereed]
This paper is concerned with the parabolic-elliptic Keller-Segel system with singular sensitivity and logistic source,{ut=Δu-χ(u/ vv)+ru-μu2,xεΩ,t>0,0=Δv-v+u,xεΩ, t>0, under homogeneous Neumann boundary conditions in a smoothly bounded domain Ω⊃ R...

Misc

 
Kentarou Fujie, Tomomi Yokota
Mathematica Bohemica   139 639-647   Jan 2014   [Refereed][Invited]
© 2014, (publisher). All rights reserved. This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function χ(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is ...
Kentarou Fujie, Takasi Senba
Proceedings of Equadiff 2017 Conference   275-282   [Refereed][Invited]
We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than (8\pi)^2, whereas the solut...
Kentarou Fujie, Takasi Senba
Proceedings of Equadiff 2017 Conference   42-52   [Refereed][Invited]
In this paper, we consider solutions to the following chemotaxis system with general sensitivity. We present a sufficient condition for the boundedness of solutions to the system and some related systems.
Kentarou Fujie, Chihiro Nishiyama, Tomomi Yokota
AIMS Proceedings, 2015   464-472   [Refereed]
This paper is concerned with global existence and boundedness of classical solutions to the quasilinear fully parabolic Keller-Segel system.

Conference Activities & Talks

 
New energy-like functional in fully parabolic systems of chemotaxis [Invited]
Kentaro Fujie
VI° Italian-Japanese Workshop GEOMETRIC PROPERTIES FOR PARABOLIC AND ELLIPTIC PDE's   20 May 2019   

Association Memberships

 
 

Social Contribution

 
Polish--Japanese Workshop on Chemotaxis
[Planner, Organizing Member]  Institute of Mathematics of the Polish Academy of Sciences  7 Dec 2018 - 8 Dec 2018