Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity

Ahn, Jaewook

doi:10.1016/j.jde.2018.11.015

Cited by 19 publications

(10 citation statements)

References 28 publications

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“…In the case that χ satisfies that χ(v) ≤ χ 0 (a+v) k (k ≥ 1, a ≥ 0), Mizukami-Yokota [16] filled in the gap between singular type and regular type, i.e., they showed that global existence and boundedness under condition χ 0 < k(a + η) k−1 2 N . Recently, Ahn [1] improved the smallness condition for χ 0 , and showed global existence and boundedness. On the other hands, if τ = 0 and χ(v) = χ 0 v with χ 0 > 2N N −2 and N ≥ 3, Nagai-Senba [17] proved that there exists some initial data u 0 such that radial solution blows up in finite time; moreover, in the case χ(v) = χ 0 v k (k ∈ (0, 1) with N ≥ 3), there exists some initial data u 0 such that radial solution blows up in finite time in [17].…”

Section: Introductionmentioning

confidence: 99%

Finite time blow-up in a parabolic-elliptic Keller-Segel system with nonlinear diffusion and signal-dependent sensitivity

Hashira

2021

Preprint

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This paper is concerned with the parabolic-elliptic Keller-Segel system with nonlinear diffusion and signal-dependent sensitivityunder homogeneous Newmann boundary conditions and initial conditions, wherefor all s > 0 and some conditions. If the case that m = 1 and χ(s) = χ 0 s −k , Nagai-Senba [17] established finite-time blow-up of solutions under the smallness conditions on a moment of initial data u(x, 0) and some condition for k ∈ (0, 1). Moreover, if the case that χ(s) ≡ (const.), Sugiyama [18] showed finite-time blow-up of solutions under the condition m ∈ [1, 2− 2 N ). According to two previous works, it seems that the smallness conditions of m and k leads to finite-time blow-up of solutions. The purpose of this paper is to give the relationship which depends only on m, k and N such that there exists initial data which corresponds finite-time blow-up solutions.

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Section: Introductionmentioning

confidence: 99%

Finite time blow-up in a parabolic-elliptic Keller-Segel system with nonlinear diffusion and signal-dependent sensitivity

Hashira

2021

Preprint

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“…where χ is a function. In this case global existence and boundedness were studied in [1,6,8,9,11,19,20,25,29,30,31]. More precisely, when 0 < χ(s) ≤ χ 0 (1+as) k for all s > 0 with some χ 0 > 0, a > 0, k > 1, Winkler [29] derived global existence and boundedness.…”

Section: Introductionmentioning

confidence: 99%

“…When 0 ≤ χ(s) ≤ χ 0 (b+s) k for all s > 0 with some small χ 0 > 0 and b ≥ 0, k ≥ 1, boundedness of classical solutions was presented in [25]. Ahn [1] improved the smallness condition for χ 0 assumed in [25], and showed stabilization (see also [31]). In the case that χ is a general function, global existence and boundedness of classical solutions were obtained in Fujie-Senba [8,9].…”

Section: Introductionmentioning

confidence: 99%

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

Chiyo¹,

Yokota²

2021

Preprint

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This paper deals with the quasilinear fully parabolic attraction-repulsion chemotaxis systemunder homogeneous Neumann boundary conditions and initial conditions, where Ω ⊂ R n (n ≥ 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 ∈ R; 0 ≤ G(s) ≤ b 0 (s + 1) q−1 with b 0 > 0 and q < min{2, m + 1}; 0 ≤ H(s) ≤ 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) ≤ χ0 s k 1 with χ 0 > 0 and k 1 > 1; 0 < ξ(s) ≤ ξ0 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 (

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“…the system possesses a global generalized solution [11]. See [1,7,12,14] for more conclusions on chemotaxis models with singular sensitivity. Consider the case of = 1 and f (u) = ru − µu k .…”

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confidence: 99%

“…Next, we give some a priori estimates of the local classical solution (u, v) to system (1). For convenience, denote T := T max .…”

mentioning

confidence: 99%

Global boundedness of classical solutions to a logistic chemotaxis system with singular sensitivity

Zhao¹

2021

DCDS-B

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Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity

Cited by 19 publications

References 28 publications

Finite time blow-up in a parabolic-elliptic Keller-Segel system with nonlinear diffusion and signal-dependent sensitivity

Finite time blow-up in a parabolic-elliptic Keller-Segel system with nonlinear diffusion and signal-dependent sensitivity

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

Global boundedness of classical solutions to a logistic chemotaxis system with singular sensitivity

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