49 citations · 59 across the 4 of their papers we have counts for
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Infinite time blow-up of solutions to the classical Keller-Segel model of chemotaxis in higher dimensions
Yūki Naito, Takasi Senba
We study the simplest parabolic-elliptic model of chemotaxis in , and show the optimal criteria for the existence of infinite time blow-up of solutions with the initial…
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 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…