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...

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, 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^{...}

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...

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...

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...

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...

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.