Chemotaxis with logistic source : Very weak global solutions and their boundedness properties

By Michael Winkler. 2008

233 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/c620b948793ae4e22b34f22f8bf9aa5ad05baf01

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Citations in the corpus

Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source (2010, background): “also [21] for less restrictive assumptions on f ).”
Biomixing by Chemotaxis and Enhancement of Biological Reactions (2011, background): “, [20, 23, 29, 31, 32] where further references can be found).”
Boundedness and global existence in the higher-dimensional parabolic–parabolic chemotaxis system with/without growth source (2015, background): “Then a lot of variants of parabolic–elliptic simplifications have been considered, see [48,14, 53,11,46] and the references therein.”
Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, background): “Winkler [55] (see also [52]) proved the global existence and boundedness of solutions to (1.”
Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source (2014, background): “In [24] the existence of (very) weak solutions is proven under more general conditions.”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, background): “We mention that also subquadratic degradation may allow for global solvability in certain modified variants of the systems, provided that its effect is suitably relative to the aggregative mechanisms of cross-diffusion and signal production ([26], [27], [36]), but counterexamples show that not any s”
An attraction‐repulsion chemotaxis system with logistic source (2016, background): “Winkler [26] studied the system{ ut = u − χ∇ · (u∇v) + λu − νuκ, 0 = v − m(t) + u (1.5) in a ball ⊂ Rn, where m(t) = 1| | ∫ u(x, t)dx.”
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction (2011, background): “2) with κ possibly being smaller than two were considered in [25], where some global ”very weak” solutions of (0.”
Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, background): “The reader is referred to [2], [7], [14], [40], [43], [45], [46], [47], [49], [50], [52], and references therein for other studies of (1.”
On the weakly competitive case in a two-species chemotaxis model (2016, background): “1) (studied in [42, 49, 50, 22]), gives rise to colorful dynamics as witnessed in e.”