Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: In two space dimensions, the parabolic-parabolic Keller-Segel system sharesmany properties with the parabolic-elliptic Keller-Segel system. Inparticular, solutions globally exist in both cases as long as their mass isless than 8?. However, this threshold is not as clear in theparabolic-parabolic case as it is in the parabolic-elliptic case, in whichsolutions with mass above 8? always blow up. Here we study forward self-similarsolutions of the parabolic-parabolic Keller-Segel system and prove that, insome cases, such solutions globally exist even if their total mass is above 8?,which is forbidden in the parabolic-elliptic case.



Author: Piotr Biler, Lucilla Corrias DP, Jean Dolbeault CEREMADE

Source: https://arxiv.org/



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