Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data

• Autorzy: Piotr Biler , Jacek Zienkiewicz
• Języki publikacji: EN

Abstrakty

EN

A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.

Kategorie tematyczne

• 35Q92: PDEs in connection with biology and other natural sciences
• 35B44: Blow-up
• 35K55: Nonlinear parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: 63
• Numer: 1
• Strony: 41-51

Daty

wydano

2015

Twórcy

autor

Piotr Biler

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Jacek Zienkiewicz

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/ba63-1-6