The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below

• Autorzy: Tomasz Cieślak
• Języki publikacji: EN

Abstrakty

EN

In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.

Kategorie tematyczne

• 35K57: Reaction-diffusion equations
• 35K60: Nonlinear initial value problems for linear parabolic equations
• 92C17: Cell movement (chemotaxis, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 74
• Numer: 1
• Strony: 127-132

Daty

wydano

2006

Twórcy

autor

Tomasz Cieślak

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc74-0-7