Parabolic System of Chemotaxis: Blowup in a Finite and the Infinite Time

By T. Senba, Takashi Suzuki. 2001

156 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Oncology

View Paper: https://www.semanticscholar.org/paper/bd7d8488250686a8b58a5648dee14e1985564295

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Citations in the corpus

Boundedness and global existence in the higher-dimensional parabolic–parabolic chemotaxis system with/without growth source (2015, unknown): “5) with g ≡ 0 and τ = 1 in a 2-D bounded domain Ω , if the initial mass ‖u0‖L1(Ω) > 4π/χ , then it is well-known [31,21,20,41] that the solution (u, v) blows up at some t = Tm ≤ ∞, and so (R1) says that ‖u(t)‖Lp(Ω) becomes unbounded when t ≈ Tm for any p > 2.”
Analysis of a chemotaxis model with indirect signal absorption (2019, background): “Its most striking feature is the possibility of chemotactic collapse; that is, the existence of solutions in spacedimension two [5, 17] and higher [27] blowing up in finite time.”
A Chemotaxis System with Logistic Source (2007, background): “…or exist globally (see, for instance, Gajewski and Zacharias, 1998; Herrero and Velázquez, 1997a,b; Horstmann and Wang, 2001; Nagai, 1995, 2001; Senba, 2005; Senba and Suzuki, 2001; cf. also Jäger and Luckhaus, 1992 for a closely related problem and Horstmann, 2003 or Suzuki, 2005 for a survey).”
Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension (2010, background): “Moreover, blow-up results for the non-symmetric two dimensional PP system on a bounded domain also exist [33, 34, 50, 51].”
How strong a logistic damping can prevent blow-up for the minimal Keller–Segel chemotaxis system? (2016, background): “A finite/infinite time blow-up never occurs in 1-dimension [15, 39, 60] (except in some extreme nonlinear denerate diffusion model [8]), a critical mass blow-up occurs in 2-dimension: when the initial mass lies below the threshold solutions exist globally, while above the threshold solutions blow up”