Searcharxiv⌕ Search

arXiv subjects

Yutaro Chiyo

Publications and source records attributed to Yutaro Chiyo.

9 recordsLinked to original sources
arXiv2023

Boundedness through nonlocal dampening effects in a fully parabolic chemotaxis model with sub and superquadratic growth

This work deals with a chemotaxis model where an external source involving a sub and superquadratic growth effect contrasted by nonlocal dampening reaction influences the motion of a cell density attracted by a chemical signal. We study the mechanism of the two densities once their initial configurations are fixed in bounded impenetrable regions; in the specific, we establish that no gathering effect for the cells can appear in time provided that the dampening effect is strong enough.

math.AP↗
arXiv2023

Global existence and boundedness in a chemotaxis-convection model with sensitivity functions for tumor angiogenesis

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)\nabla v) +\nabla \cdot (uχ_2(w)\nabla w), &x \in Ω,\ t>0, \\[1.05mm] v_t=Δv+\nabla \cdot (vξ(w)\nabla w)+αu-βv, &x \in Ω,\ t>0, \\[1.05mm] w_t=Δw+γu-δw, &x \in Ω,\ t>0 \end{cases} \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $Ω\subset \mathbb{R}^n$ $(n \le 3)$ is a bounded domain with smooth boundary, $χ_1, χ_2, ξ$ are functions satisfying some conditions and $α, β, γ, δ>0$ are constants. The purpose of this paper is to establish global existence and boundedness in this system.

math.AP↗
arXiv2022

Stabilization for small mass in a quasilinear parabolic--elliptic--elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: repulsion-dominant case

This paper deals with the quasilinear attraction-repulsion chemotaxis system \begin{align*} \begin{cases} u_t=\nabla\cdot \big((u+1)^{m-1}\nabla u -χu(u+1)^{p-2}\nabla v +ξu(u+1)^{q-2}\nabla w\big),\\[] 0=Δv+αu-βv,\\[] 0=Δw+γu-δw \end{cases} \end{align*} in a bounded domain $Ω\subset \mathbb{R}^n$ $(n \in \mathbb{N})$ with smooth boundary $\partial Ω$, where $m, p, q \in \mathbb{R}$, $χ, ξ, α, β, γ, δ>0$ are constants. In the case that $m=1$ and $p=q=2$, when $χα-ξγ<0$ and $β=δ$, Tao-Wang (Math. Models Methods Appl. Sci.; 2013; 23; 1-36) proved that global bounded classical solutions toward the spatially constant equilibrium $(\overline{u_0}, \fracαβ\overline{u_0}, \fracγδ\overline{u_0})$ via the reduction to the Keller-Segel system by using the transformation $z:=χv-ξw$, where $\overline{u_0}$ is the spatial average of the initial data $u_0$. However, since the above system involves nonlinearities, the method is no longer valid. The purpose of this paper is to establish that global bounded classical solutions converge to the spatially constant equilibrium $(\overline{u_0}, \fracαβ\overline{u_0}, \fracγδ\overline{u_0})$.

math.AP↗
arXiv2021

Boundedness in a fully parabolic attraction-repulsion chemotaxis system with nonlinear diffusion and signal-dependent sensitivity

This paper deals with the quasilinear fully parabolic attraction-repulsion chemotaxis system \begin{align*} u_t=\nabla \cdot (D(u)\nabla u) -\nabla \cdot (G(u)χ(v)\nabla v) +\nabla\cdot(H(u)ξ(w)\nabla w), \quad v_t=d_1Δv+αu-βv, \quad w_t=d_2Δw+γu-δw, \quad x \in Ω,\ t>0, \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $Ω\subset \mathbb{R}^n$ $(n \ge 1)$ is a bounded domain with smooth boundary, $d_1, d_2, α, β, γ, δ>0$ are constants. Also, the diffusivity $D$, the density-dependent sensitivities $G, H$ fulfill $D(s)=a_0(s+1)^{m-1}$ with $a_0>0$ and $m \in \mathbb{R}$; $0 \le G(s) \le b_0(s+1)^{q-1}$ with $b_0>0$ and $q<\min\{2,\ m+1\}$; $0 \le H(s) \le c_0(s+1)^{r-1}$ with $c_0>0$ and $r<\min\{2,\ m+1\}$, and the signal-dependent sensitivities $χ, ξ$ satisfy $0<χ(s)\le \frac{χ_0}{s^{k_1}}$ with $χ_0>0$ and $k_1>1$; $0<ξ(s)\le \frac{ξ_0}{s^{k_2}}$ with $ξ_0>0$ and $k_2>1$. Global existence and boundedness in the case that $w=0$ were proved by Ding (J. Math. Anal. Appl.; 2018;461;1260-1270) and Jia-Yang (J. Math. Anal. Appl.; 2019;475;139-153). However, there is no work on the above fully parabolic attraction-repulsion chemotaxis system with nonlinear diffusion and signal-dependent sensitivity. This paper develops global existence and boundedness of classical solutions to the above system by introducing a new test function.

math.AP↗
arXiv2021

Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system

This paper deals with the quasilinear attraction-repulsion chemotaxis system \begin{align*} \begin{cases} u_t=\nabla\cdot \big((u+1)^{m-1}\nabla u -χu(u+1)^{p-2}\nabla v +ξu(u+1)^{q-2}\nabla w\big) +f(u), \\[1.05mm] 0=Δv+αu-βv, \\[1.05mm] 0=Δw+γu-δw \end{cases} \end{align*} in a bounded domain $Ω\subset \mathbb{R}^n$ ($n \in \mathbb{N}$) with smooth boundary $\partialΩ$, where $m, p, q \in \mathbb{R}$, $χ, ξ, α, β, γ, δ>0$ are constants. Moreover, it is supposed that the function $f$ satisfies $f(u)\equiv0$ in the study of boundedness, whereas, when considering blow-up, it is assumed that $m>0$ and $f$ is a function of logistic type such as $f(u)=λu-μu^κ$ with $λ\ge 0$, $μ>0$ and $κ>1$ sufficiently close to~$1$, in the radially symmetric setting. In the case that $ξ=0$ and $f(u) \equiv 0$, global existence and boundedness have been proved under the condition $p 0$. This paper classifies boundedness and blow-up into the cases $p q$ without any condition for the sign of $χα-ξγ$ and the case $p=q$ with $χα-ξγ<0$ or $χα-ξγ>0$.

math.AP↗
arXiv2021

Remarks on finite-time blow-up in a fully parabolic attraction-repulsion chemotaxis system via reduction to the Keller-Segel system

This paper deals with the fully parabolic attraction-repulsion chemotaxis system \begin{align*} u_t=Δu-χ\nabla \cdot (u\nabla v)+ξ\nabla\cdot(u \nabla w), \quad v_t=Δv-v+u, \quad w_t=Δw-w+u, \quad x \in Ω,\ t>0 \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $Ω$ is an open ball in $\mathbb{R}^n$ ($n \ge 3$), $χ, ξ>0$ are constants. When $w=0$, finite-time blow-up in the corresponding Keller-Segel system has already been obtained. However, finite-time blow-up in the above attraction-repulsion chemotaxis system has not yet been established except for the case $n=3$. This paper provides an answer to this open problem by using a transformation which leads to a system presenting structural advantages respect to the original.

math.AP↗
arXiv2021

Global existence and boundedness in a fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities without logistic source

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 v) +\nabla \cdot (uξ(w)\nabla w), &x \in Ω,\ t>0,\\[1.05mm] v_t=Δv-v+u, &x \in Ω,\ t>0,\\[1.05mm] w_t=Δw-w+u, &x \in Ω,\ t>0 \end{cases} \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $Ω\subset \mathbb{R}^n$ $(n \ge 2)$ is a bounded domain with smooth boundary, $χ, ξ$ are functions satisfying some conditions. Global existence and boundedness of classical solutions to the system with logistic source have already been obtained by taking advantage of the effect of logistic dampening (J. Math. Anal. Appl.; 2020;489;124153). This paper establishes existence of global bounded classical solutions despite the loss of logistic dampening.

math.AP↗
arXiv2021

Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with superlinear logistic degradation

This paper is concerned with the attraction-repulsion chemotaxis system with superlinear logistic degradation, \begin{align*} \begin{cases} u_t = Δu - χ\nabla\cdot(u \nabla v) + ξ\nabla\cdot (u \nabla w) + λu - μu^k, \quad &x \in Ω,\ t>0,\\[1.05mm] 0= Δv + αu - βv, \quad &x \in Ω,\ t>0,\\[1.05mm] 0= Δw + γu - δw, \quad &x \in Ω,\ t>0, \end{cases} \end{align*} under homogeneous Neumann boundary conditions, in a ball $Ω\subset \mathbb{R}^n$ ($n \ge 3$), with constant parameters $λ\in \mathbb{R}$, $k>1$, $μ, χ, ξ, α, β, γ, δ>0$. Blow-up phenomena in the system have been well investigated in the case $λ=μ=0$, whereas the attraction-repulsion chemotaxis system with logistic degradation has been not studied. Under the condition that $k>1$ is close to $1$, this paper ensures a solution which blows up in $L^\infty$-norm and $L^σ$-norm with some $σ>1$ for some nonnegative initial data. Moreover, a lower bound of blow-up time is derived.

math.AP↗