TY - JOUR
T1 - The set of concentration for some hyperbolic models of chemotaxis
AU - Derbel, Lobna
AU - Jabin, Pierre Emmanuel
PY - 2007/6
Y1 - 2007/6
N2 - Chemotaxis models are typically able to develop blow-up in finite times. For some specific models, we obtain some estimates on the set of concentration of cells (defined roughly as the points where the density of cells is infinite with a non-vanishing mass). More precisely we consider models without diffusion for which the cells' velocity decreases if the concentration of the chemical attractant becomes too large. We are able to give a lower bound on the Hausdorff dimension of the concentration set, one in the "best" situation where the velocity exactly vanishes for too large concentrations of attractant. This in particular implies that the solution may not form any Dirac mass.
AB - Chemotaxis models are typically able to develop blow-up in finite times. For some specific models, we obtain some estimates on the set of concentration of cells (defined roughly as the points where the density of cells is infinite with a non-vanishing mass). More precisely we consider models without diffusion for which the cells' velocity decreases if the concentration of the chemical attractant becomes too large. We are able to give a lower bound on the Hausdorff dimension of the concentration set, one in the "best" situation where the velocity exactly vanishes for too large concentrations of attractant. This in particular implies that the solution may not form any Dirac mass.
UR - http://www.scopus.com/inward/record.url?scp=34249844137&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34249844137&partnerID=8YFLogxK
U2 - 10.1142/S021989160700115X
DO - 10.1142/S021989160700115X
M3 - Article
AN - SCOPUS:34249844137
SN - 0219-8916
VL - 4
SP - 331
EP - 349
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 2
ER -