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| It is well known that the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular non- negative solutions with total mass below the critical value $8\pi.$ Solutions with mass above $8\pi$ blow up in a finite time. Here we study the case of the parabolic-parabolic Keller-Segel where we proved that each mass may lead to a global-in-time-solution, even if the initial data is a finite signed measure. |
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