57 citations · 163 across the 18 of their papers we have counts for
22 papers
Global existence and boundedness in a chemotaxis-convection model with sensitivity functions for tumor angiogenesis
Yutaro Chiyo, Masaaki Mizukami
This paper deals with the fully parabolic chemotaxis-convection model with sensitivity functions for tumor angiogenesis, \begin{align*} \begin{cases} u_t=Δu-\nabla \cdot (uχ_1(v)\n…
Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source
Tobias Black, Mario Fuest, Johannes Lankeit +1
We discuss the influence of possible spatial inhomogeneities in the coefficients of logistic source terms in parabolic-elliptic chemotaxis-growth systems of the form \begin{align*}…
Can chemotactic effects lead to blow-up or not in two-species chemotaxis-competition models?
Masaaki Mizukami, Yuya Tanaka, Tomomi Yokota
This paper deals with the two-species chemotaxis-competition models \begin{align*} \begin{cases} u_t = d_1 Δu - χ_1 \nabla \cdot (u \nabla w) + μ_1 u (1- u^{κ_1-1} - a_1 v^{λ_1-1})…
Global existence and boundedness in a fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities without logistic source
Yutaro Chiyo, Masaaki Mizukami, Tomomi Yokota
This paper deals with the fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities, \begin{align*} \begin{cases} u_t=Δu-\nabla \cdot (uχ(v)\nabla…
Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model
Mario Fuest, Johannes Lankeit, Masaaki Mizukami
Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*} n_t &= Δn - \nabla \cdot (n \nabla c), \\ 0 &= Δc - nc, \end{align*} un…
Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation
Yuka Chiyoda, Masaaki Mizukami, Tomomi Yokota
This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \begin{align*} \begin{cases} u_t = \nabla\cdot\left(\dfrac{u^p \nabla u}{\sqrt{u^2 + |\nabla…
Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation
Masaaki Mizukami, Tatsuhiko Ono, Tomomi Yokota
This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \begin{equation*} \begin{cases} u_t = \nabla\cdot\left(\dfrac{u^p \nabla u}{\sqrt{u^2 + |\na…
Stabilization in the Keller--Segel system with signal-dependent sensitivity
Tobias Black, Johannes Lankeit, Masaaki Mizukami
This paper deals with the Keller--Segel system with signal-dependent sensitivity \begin{align*} &u_t = Δu - χ\nabla \cdot (uS(v)\nabla v), &v_t = Δv - v + u, \end{align*} where $χ>…
How strongly does diffusion or logistic-type degradation affect existence of global weak solutions in a chemotaxis-Navier--Stokes system?
Masaaki Mizukami
This paper considers the chemotaxis-Navier--Stokes system with nonlinear diffusion and logistic-type degradation term \begin{align*} \begin{cases} n_t + u\cdot\nabla n = \nabla \cd…
A Keller-Segel-fluid system with singular sensitivity: Generalized solutions
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In bounded smooth domains , , we consider the Keller-Segel-Stokes system \begin{align*} n_t + u\cdot \nabla n &= Δn - χ\nabla \cdot(\frac{n}{c}\n…
Global weak solutions to a 3-dimensional degenerate and singular chemotaxis-Navier--Stokes system with logistic source
Shunsuke Kurima, Masaaki Mizukami
This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term , $x \in Ω,\ t…
The fast signal diffusion limit in a Keller-Segel system
Masaaki Mizukami
This paper deals with convergence of a solution for the parabolic-parabolic Keller-Segel system \[ (u_λ)_t = Δu_λ- χ\nabla \cdot (u_λ\nabla v_λ), \quad λ(v_λ)_t = Δv_λ- v_λ+ u_λ\qu…
The fast signal diffusion limit in a chemotaxis system with strong signal sensitivity
Masaaki Mizukami
This paper gives a first insight into making a mathematical bridge between the parabolic-parabolic signal-dependent chemotaxis system and its parabolic-elliptic version. To be more…
Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier--Stokes system with competitive kinetics
Misaki Hirata, Shunsuke Kurima, Masaaki Mizukami +1
This paper is concerned with the 3-dimensional two-species chemotaxis-Navier--Stokes system with Lotka--Volterra competitive kinetics under homogeneous Neumann boundary conditions…
Singular sensitivity in a Keller-Segel-fluid system
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In bounded smooth domains , , considering the chemotaxis--fluid system \[ \begin{cases} \begin{split} & n_t + u\cdot \nabla n &= Δn - χ\nabla \cd…
Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller--Segel-Stokes system with competitive kinetics
Xinru Cao, Shunsuke Kurima, Masaaki Mizukami
This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\cdot\nabla n_1 =Δn_1 - χ_1\nabla\cdot(n_1\nabla c)+ μ_1n_1(1- n_1 - a_1n_2)…
Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
Masaaki Mizukami
This paper deals with the two-species chemotaxis-competition system. About the problem, Bai--Winkler first obtained asymptotic stability under some conditions. Recently, the condit…
Boundedness and stabilization in a two-species chemotaxis-competition system of parabolic-parabolic-elliptic type
Masaaki Mizukami
This paper deals with the two-species chemotaxis-competition system , $v_t = d_2 Δv - χ_2 \nabla \cdot (v \nabl…
Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics
Xinru Cao, Shunsuke Kurima, Masaaki Mizukami
This paper considers the two-species chemotaxis-Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a three-dimensional bounded domain with smo…
A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity
Masaaki Mizukami, Tomomi Yokota
This paper deals with the Keller--Segel system with signal-dependent sensitivity \begin{equation*} u_t=Δu - \nabla \cdot (u χ(v)\nabla v), \quad v_t=Δv + u - v, \quad x\inΩ,\ t>0,…
How far does small chemotactic interaction perturb the Fisher-KPP dynamics?
Johannes Lankeit, Masaaki Mizukami
This paper deals with nonnegative solutions of the Neumann initial-boundary value problem for the fully parabolic chemotaxis-growth system $=Δu_{\varepsilon}…
On the weakly competitive case in a two-species chemotaxis model
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady sta…