The $8\pi$-problem for radially symmetric solutions of a chemotaxis model in a disc

By Piotr Biler, Grzegorz Karol Karch, Philippe Laurençot, T. Nadzieja. 2006

69 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/65707f3c4ce2516f71b1213ee494f2ad162d013d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Piotr Biler
2. Grzegorz Karol Karch
3. Philippe Laurençot
4. Juan Luis V'azquez
5. Lucilla Corrias
6. Adrien Blanchet

In Modeling and Simulation

1. Grzegorz Karol Karch
2. Piotr Biler
3. Philippe Laurençot
4. Lucilla Corrias
5. Michael Winkler
6. Adrien Blanchet
7. P. Lemari'e-Rieusset

Citations in the corpus

• Critical space for the parabolic-parabolic Keller–Segel model in Rd (2006, unknown): “In dimension d = 2, L 1 ( R d ) is the critical space: for M below the critical mass 8 π/χ there are global weak solutions, for M above the critical mass there is blow-up in finite time [6,2,13,1].”
• The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane (2006, background): “We infer from (2.19) that, if R ≥ Sε(T ), we have |IR(T )− IR(0)| ≤ 2 ε T C(ζ) , from which we deduce that lim R→∞ |IR(T )− IR(0)| = 0 .”