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.

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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 -