Diffusion-dominated asymptotics of solution to chemotaxis model

Raczyński, A.

doi:10.1007/s00028-011-0099-x

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…System (1.1) is already studied in the whole space e.g. in the papers [4][5][6]13,14,16,17,19], where several results either on a blow-up or on a large-time behavior of solutions have been obtained.…”

Section: Introductionmentioning

confidence: 99%

Stability of constant steady states of a chemotaxis model

et al. 2021

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The Cauchy problem for the parabolic–elliptic Keller–Segel system in the whole n-dimensional space is studied. For this model, every constant $$A \in {\mathbb {R}}$$ A ∈ R is a stationary solution. The main goal of this work is to show that $$A < 1$$ A < 1 is a stable steady state while $$A > 1$$ A > 1 is unstable. Uniformly local Lebesgue spaces are used in order to deal with solutions that do not decay at spatial variable on the unbounded domain.

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Section: Introductionmentioning

confidence: 99%

Stability of constant steady states of a chemotaxis model

et al. 2021

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“…System (1.1) was already studied in the whole space e.g. in the papers [4,5,6,13,14,16,17,19], where several results either on a blow up or on a large time behavior of solutions have been obtained. For each constant A ∈ R, the couple (u, ψ) = (A, A) is a stationary solution of system (1.1) and, since the domain is unbounded, it does not belong to any Lebesgue L pspace with p ∈ [1, ∞).…”

Section: Introductionmentioning

confidence: 99%

Stability of constant steady states of a chemotaxis model

Cygan

Karch

Krawczyk

et al. 2021

Preprint

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The Cauchy problem for the parabolic-elliptic Keller-Segel system in the whole n-dimensional space is studied. For this model, every constant A ∈ R is a stationary solution. The main goal of this work is to show that A < 1 is a stable steady state while A > 1 is unstable. Uniformly local Lebesgue spaces are used in order to deal with solutions that do not decay at spatial variable on the unbounded domain.

show abstract