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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles Blow up of solutions to generalized Keller--Segel model Global Existence and Finite Time Blow-Up for Critical Patlak-Keller-Segel Models with Inhomogeneous Diffusion A study of blow-ups in the Keller-Segel model of chemotaxis Stable blow-up dynamic for the parabolic-parabolic Patlak-Keller-Segel model The fractional Keller-Segel model Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up Measure valued solutions of the 2D Keller-Segel system Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension Exact criterion for global existence and blow up to a degenerate Keller-Segel system Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system More... Mathematics 2013 # Sharp Condition for blow-up and global existence in a two species chemotactic Keller-Segel system in$\mathbb{R}^2\$

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Abstract:

For the parabolic-elliptic Keller-Segel system in R^2 it has been proved that if the initial mass is less than 8\pi/\chi\ global solution exist and in the case that the initial mass is larger than 8\pi/\chi\ blow-up happens. The case of several chemotactic species introduces an additional question: What is the analog for the critical mass obtained for the single species system? We find a threshold curve in the case of two especies case that allows us to determine if the system has blow-up or has a global in time solution.

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