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

Chiyo, Yutaro; Marras, Monica; Tanaka, Yuya; Yokota, Tomomi

doi:10.1016/j.na.2021.112550

Cited by 16 publications

(5 citation statements)

References 27 publications

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“…Further, from the stricter mathematical point of view, when D(u) u m1 , S(u) u m2 , T (u) u m3 and h(u) λu − μu β (where m 1 , m 2 , m 3 , λ, μ, β attain some real values), we mention that for linear and nonlinear productions, criteria toward boundedness, long time behaviors and blow-up issues for related solutions to (3) when τ 1 , τ 2 ∈ {0, 1} can be found in [3,8,11,19,25,26,29,31,32,38,39].…”

Section: The Attraction-repulsion Model: Combining Effectsmentioning

confidence: 99%

Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption

Frassu

Viglialoro

2023

Z. Angew. Math. Phys.

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This paper is framed in a series of studies on attraction–repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or production impacts, for those of the chemicals. In particular, herein we focus on the situation where the signal responsible of gathering tendencies for the particles’ distribution is produced, while the opposite counterpart is consumed. In such a sense, this research complements the results in Frassu et al. (Math Methods Appl Sci 45:11067–11078, 2022) and Chiyo et al. (Commun Pure Appl Anal, 2023, doi: 10.3934/cpaa.2023047), where the chemicals evolve according to different laws.

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Section: The Attraction-repulsion Model: Combining Effectsmentioning

confidence: 99%

Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption

Frassu

Viglialoro

2023

Z. Angew. Math. Phys.

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“…Also, in the simplified case that τ = 0 there are more precise studies. Indeed, blow-up with logistic source was discussed in [2] and stabilization was investigated in [10,13]. On the other hand, as to the quasilinear version, such as (1.1), of the above system (1.4) with τ = 0, there are several studies.…”

Section: Y Chiyomentioning

confidence: 99%

Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

Chiyo¹

2023

Arch. Math. (Brno)

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“…When

h=h_k\not\equiv 0

, for both linear and nonlinear productions scenarios, and stationary or evolutive equations (formally,

P^{\tau }_\alpha (v)=Q^{\tau }_\beta (w)=0

), criteria toward boundedness, long time behaviors, and blow‐up issues for related solutions are studied in Refs. [20–23].…”

Section: Introduction Motivations and State Of The Artmentioning

confidence: 99%

Properties of given and detected unbounded solutions to a class of chemotaxis models

2023

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This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction–repulsion model, with nonlinear productions, diffusion, sensitivities, and logistic term, we detect Lebesgue spaces where given unbounded solutions also blow up in the corresponding norms of those spaces; subsequently, estimates for the blow‐up time are established. Finally, for a simplified version of the model, some blow‐up criteria are proved.More precisely, we analyze a zero‐flux chemotaxis system essentially described as The problem is formulated in a bounded and smooth domain Ω of , with , for some , , , and with . A sufficiently regular initial data is also fixed.Under specific relations involving the above parameters, one of these always requiring some largeness conditions on , we prove that any given solution to (), blowing up at some finite time becomes also unbounded in ‐norm, for all ; we give lower bounds T (depending on ) of for the aforementioned solutions in some ‐norm, being ; whenever , we establish sufficient conditions on the parameters ensuring that for some u0 solutions to () effectively are unbounded at some finite time. Within the context of blow‐up phenomena connected to problem (), this research partially improves the analysis in Wang et al. (J Math Anal Appl. 2023;518(1):126679) and, moreover, contributes to enrich the level of knowledge on the topic.

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

Cited by 16 publications

References 27 publications

Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption

Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption

Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

Properties of given and detected unbounded solutions to a class of chemotaxis models

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