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@ARTICLE{Fuhrmann:910531,
      author       = {Fuhrmann, Jan and Lankeit, Johannes and Winkler, Michael},
      title        = {{A} double critical mass phenomenon in a
                      no-flux-{D}irichlet {K}eller-{S}egel system},
      journal      = {Journal de mathématiques pures et appliquées},
      volume       = {162},
      issn         = {0021-7824},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier},
      reportid     = {FZJ-2022-03913},
      pages        = {124 - 151},
      year         = {2022},
      note         = {ISSN 0021-7824 not unique: **2 hits**.},
      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.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000798180300004},
      doi          = {10.1016/j.matpur.2022.04.004},
      url          = {https://juser.fz-juelich.de/record/910531},
}