49 citations · 90 across the 8 of their papers we have counts for
9 papers
Nonlinear Fisher information, corresponding functional inequalities and applications
Tomasz Cieślak, Kentaro Fujie, Tatsuya Hosono
We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality…
Global boundedness of solutions to a parabolic-parabolic chemotaxis system with local sensing in higher dimensions
Kentaro Fujie, Takasi Senba
This paper deals with classical solutions to the parabolic-parabolic system \begin{align*} \begin{cases} u_t=Δ(γ(v) u ) &\mathrm{in}\ Ω\times(0,\infty), \\[1mm] v_t=Δv - v + u &\ma…
Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions
Kentaro Fujie, Takasi Senba
This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller--Segel system,…
Boundedness of Classical Solutions to a Degenerate Keller--Segel Type Model with Signal-dependent Motilities
Kentaro Fujie, Jie Jiang
In this paper, we consider the initial Neumann boundary value problem for a degenerate kinetic model of Keller--Segel type. The system features a signal-dependent decreasing motili…
Comparison Methods for a Keller--Segel-type Model of Pattern Formations with Density-suppressed Motilities
Kentarou Fujie, Jie Jiang
This paper is concerned with global existence as well as infinite-time blowups of classical solutions to the following fully parabolic kinetic system \begin{equation} \begin{cases}…
Global Existence for a Kinetic Model of Pattern Formation with Density-suppressed Motilities
Kentarou Fujie, Jie Jiang
In this paper, we consider global existence of classical solutions to the following kinetic model of pattern formation \begin{equation} \begin{cases} u_t=Δ(γ(v)u)+μu(1-u) -Δv+v=u \…
Boundedness of solutions to the critical fully parabolic quasilinear one-dimensional Keller-Segel system
Bartosz Bieganowski, Tomasz Cieślak, Kentarou Fujie +1
In this paper we consider a one-dimensional fully parabolic quasilinear Keller-Segel system with critical nonlinear diffusion. We show uniform-in-time boundedness of solutions, whi…
No critical nonlinear diffusion in 1D quasilinear fully parabolic chemotaxis system
Tomasz Cieślak, Kentarou Fujie
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 c…
Global existence in the 1D quasilinear parabolic-elliptic chemotaxis system with critical nonlinearity
Tomasz Cieślak, Kentarou Fujie
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 i…