Title:Boundedness of global classical solutions for a chemotaxis system with signal-dependent motility and nutrient consumption
Speaker:Yuxiang Li（Southeast University）
Time:Thursday, December28, 2023, 09:30-11:30
Location: B201-1, Mingde Building
Tecent meeting, Meeting ID：677-111-380, Password：160718
Abstract：In this talk we consider the initial-boundary value problem for a Keller-Segel system with the logistic term 
. The Keller-Segel system describes directional movement of bacteria caused by the signal-dependent diffusion and the starvation driven diffusion. We prove that
1) The signal production equation is elliptic. If 
or 
and 
is sufficiently large, then the classical solutions of the system are globally bounded in dimensions 
. On the other hand, if 
, we obtain the global existence of weak solutions to the system when 
.
2) The signal production equation is parabolic. If 
or 
and 
is sufficiently large, then the classical solutions of the system are globally bounded when 
. On the other hand, if 
, we obtain the global existence of weak solutions to the system when 
. In comparison with the case that the signal production equation is elliptic, here 
.
3) When the signal production equation is elliptic or parabolic, if 
, we obtain the uniform boundedness of global classical solutions to the system with 
.
