Masaaki Mizukami

Boundedness and stabilization in a two-species chemotaxis-competition system of parabolic-parabolic–elliptic type

This paper is concerned with the two-species chemotaxis-competition system ut=d1Δu−χ1∇·(u∇w)+μ1u(1−u−a1v)inΩ×(0,∞),vt=d2Δv−χ2∇·(v∇w)+μ2v(1−a2u−v)inΩ×(0,∞),0=d3Δw+αu+βv−γwinΩ×(0,∞), where Ω is a bounded domain in Rn with smooth boundary ∂Ω, n≥2; χi and μi are constants satisfying some conditions. The above system was studied in the cases that a1,a2∈(0,1) and a1>1>a2, and it was proved that global existence and asymptotic stability hold when χiμi are small. However, the conditions in the above 2 cases strongly depend on a1,a2, and have not been obtained in the case that a1,a2≥1. Moreover, convergence rates in the cases that a1,a2∈(0,1) and a1>1>a2 have not been studied. The purpose of this work is to construct conditions which derive global existence of classical bounded solutions for all a1,a2>0 which covers the case that a1,a2≥1, and lead to convergence rates for solutions of the above system in the cases that a1,a2∈(0,1) and a1≥1>a2.

Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics: Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics

This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics

Singular sensitivity in a Keller–Segel-fluid system

(n_1)_t + u\cdot\nabla n_1 =\Delta n_1 - \chi_1\nabla\cdot(n_1\nabla c)+ \mu_1n_1(1- n_1 - a_1n_2)

On the weakly competitive case in a two-species chemotaxis model

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Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion

(n_2)_t + u\cdot\nabla n_2 =\Delta n_2 - \chi_2\nabla\cdot(n_2\nabla c) + \mu_2n_2(1- a_2n_1 - n_2), c_t + u\cdot\nabla c =\Delta c - c + \alpha n_1 +\beta n_2

A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity

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Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier–Stokes system with competitive kinetics

u_t= \Delta u + \nabla P+ (\gamma n_1 + \delta n_2)\nabla\phi

Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller--Segel-Stokes system with competitive kinetics

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How far does small chemotactic interaction perturb the Fisher–KPP dynamics?

\nabla\cdot u = 0

The fast signal diffusion limit in a chemotaxis system with strong signal sensitivity

under homogeneous Neumann boundary conditions in a bounded domain