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arXiv · 1401.7650

Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane

Piotr Biler·Ignacio Guerra·Grzegorz Karch
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Abstract

As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value $8π$. Solutions with mass above $8π$ blow up in a finite time. We show that the case of the parabolic-parabolic Keller-Segel is different: each mass may lead to a global-in-time-solution, even if the initial data is a finite signed measure. These solutions need not be unique, even if we limit ourselves to nonnegative solutions.

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Piotr Biler, Ignacio Guerra, Grzegorz Karch. 2014-01-29. Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane. https://arxiv.org/abs/1401.7650

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