Blow-up in a chemotaxis model without symmetry assumptions

By Dirk Horstmann, Guofang Wang. European journal of applied mathematics, 2001

484 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/0c728d7c7e6a27b9481837e9c1c3df8d9ae8831c

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Citations in the corpus

The one‐dimensional chemotaxis model: global existence and asymptotic profile (2004, unknown): “References [3–8]).”
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): “…question whether solutions blow up in finite time 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…”
Boundedness of the attraction–repulsion Keller–Segel system (2015, background): “This particular structure motivated a vast amount of mathematical studies in the past (see review articles [7,9,27]) and recent studies [3,8,26,28,29], where most of works were focused at whether the solution blows up or not (see some early works in [10,19,20] in this area).”
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system (2011, background): “1) with mass satisfying m < 4π remain bounded for all times ([12], [29]), while for any ε > 0 there exist some unbounded solutions mith mass m < 4π + ε ([18]).”
Boundedness, blowup and critical mass phenomenon in competing chemotaxis (2016, methodology): “6 or see [16]), where G(·, 0) satisfies {− G + βG = δ0, x ∈ Ur, ∂G ∂ν = 0, x ∈ ∂Ur, with δ0 denoting the Dirac measure on Ur giving unit mass to the point 0.”
Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, background): “·(nχ∇c), αct = ∆c−τc+n, n(x,0) = n0(x), c(x,0) = c0(x), (1.2) where χis the sensitivity and τ−12 represents the activation length. The system in (1.2) has been extensively studied by many authors(see [9, 10, 15, 16, 21] and references therein). For the chemical consumption model by the cell or bacte”
A critical blow-up exponent in a chemotaxis system with nonlinear signal production (2018, background): “1) and parabolic-elliptic simplifications thereof, and clarifying that such explosion phenomena may occur therein if and only if the spatial setup is two- or higher-dimensional [19, 21, 22, 25, 35, 49], in the past few years the analysis has proceeded to involve corresponding questions for more elab”
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production (2016, unknown): “[15] for a partial result on unboundedness).”