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000910531 1001_ $$0P:(DE-Juel1)184603$$aFuhrmann, Jan$$b0$$eCorresponding author
000910531 245__ $$aA double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system
000910531 260__ $$aAmsterdam [u.a.]$$bElsevier$$c2022
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000910531 520__ $$aDerived from a biophysical model for the motion of a crawling cell, the evolution system(⋆) is investigated in a finite domain , , with . Whereas a comprehensive literature is available for cases in which (⋆) describes chemotaxis-driven population dynamics and hence is accompanied by homogeneous Neumann-type boundary conditions for both components, the presently considered modeling context, besides yet requiring the flux to vanish on ∂Ω, inherently involves homogeneous Dirichlet boundary conditions for the attractant v, which in the current setting corresponds to the cell's cytoskeleton being free of pressure at the boundary. This modification in the boundary setting is shown to go along with a substantial change with respect to the potential to support the emergence of singular structures: It is, inter alia, revealed that in contexts of radial solutions in balls there exist two critical mass levels, distinct from each other whenever or , that separate ranges within which (i) all solutions are global in time and remain bounded, both global bounded and exploding solutions exist, or all nontrivial solutions blow up. While critical mass phenomena distinguishing between regimes of type (i) and belong to the well-understood characteristics of (⋆) when posed under classical no-flux boundary conditions in planar domains, the discovery of a distinct secondary critical mass level related to the occurrence of seems to have no nearby precedent. In the planar case with the domain being a disk, the analytical results are supplemented with some numerical illustrations, and it is discussed how the findings can be interpreted biophysically for the situation of a cell on a flat substrate.
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000910531 588__ $$aDataset connected to CrossRef, Journals: juser.fz-juelich.de
000910531 7001_ $$0P:(DE-HGF)0$$aLankeit, Johannes$$b1
000910531 7001_ $$0P:(DE-HGF)0$$aWinkler, Michael$$b2
000910531 773__ $$0PERI:(DE-600)1479500-0$$a10.1016/j.matpur.2022.04.004$$gVol. 162, p. 124 - 151$$p124 - 151$$tJournal de mathématiques pures et appliquées$$v162$$x0021-7824$$y2022
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