Journal Article

FZJ-2022-03913

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system

Fuhrmann, J. (Corresponding author)FZJ* ; Lankeit, J. ; Winkler, M.

2022
Elsevier Amsterdam [u.a.]

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Please use a persistent id in citations: http://hdl.handle.net/2128/32199  doi:10.1016/j.matpur.2022.04.004

Abstract: Derived from a biophysical model for the motion of a crawling cell, the evolution system(⋆) is investigated in a finite domain , , with . Whereas a comprehensive literature is available for cases in which (⋆) describes chemotaxis-driven population dynamics and hence is accompanied by homogeneous Neumann-type boundary conditions for both components, the presently considered modeling context, besides yet requiring the flux to vanish on ∂Ω, inherently involves homogeneous Dirichlet boundary conditions for the attractant v, which in the current setting corresponds to the cell's cytoskeleton being free of pressure at the boundary. This modification in the boundary setting is shown to go along with a substantial change with respect to the potential to support the emergence of singular structures: It is, inter alia, revealed that in contexts of radial solutions in balls there exist two critical mass levels, distinct from each other whenever or , that separate ranges within which (i) all solutions are global in time and remain bounded, both global bounded and exploding solutions exist, or all nontrivial solutions blow up. While critical mass phenomena distinguishing between regimes of type (i) and belong to the well-understood characteristics of (⋆) when posed under classical no-flux boundary conditions in planar domains, the discovery of a distinct secondary critical mass level related to the occurrence of seems to have no nearby precedent. In the planar case with the domain being a disk, the analytical results are supplemented with some numerical illustrations, and it is discussed how the findings can be interpreted biophysically for the situation of a cell on a flat substrate.

Note: ISSN 0021-7824 not unique: **2 hits**.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2022

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