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Ponte Academic Journal
Jun 2017, Volume 73, Issue 6

THE -ZITI'S METHOD TO DETECT THE BLOW-UP IN FINITE TIME IN SOME MODELS OF CHEMOTAXIS.

Author(s): Larbi BSISS ,Cherif Ziti

J. Ponte - Jun 2017 - Volume 73 - Issue 6
doi: 10.21506/j.ponte.2017.6.20



Abstract:
We consider a class of models of chemotactic bacterial populations, introduced by Keller-Segel. For those models, we investigate the possibility of chemotactic collapse, in other words, the possibility that in nite time the population of predators aggregates to form a delta-function (Dirac). To study this phenomenon, we applied the new numerical approximation called ziti's -method, which may or may not blow-up (in nite time), depending on the relative strength of three mechanisms in competition: (i) the chemotactic attraction of bacteria towards regions of high concentration in substrate (ii) the rate of consumption of the substrate by the bacteria and (iii) (possibly) the diusion of bacteria or the substrate. Our results are compared by the self similar (exact solution) obtained in [25].
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