Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2025

Upper bounds for the blow-up time of the 2-d parabolic-elliptic Patlak-Keller-Segel model of chemotaxis

Patrick Maheux
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Résumé

In this paper, we obtain upper bounds for the critical time T * of the blowup for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. Such estimates is rarely obtained and discuss in the papers on the subject No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the mass is assumed. The result is expressed not only in terms of the supercritical mass M > 8π, but also in terms of the shape of the initial data.

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hal-04139369 , version 1 (23-06-2023)

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Patrick Maheux. Upper bounds for the blow-up time of the 2-d parabolic-elliptic Patlak-Keller-Segel model of chemotaxis. Journal of Mathematical Analysis and Applications, 2025, 549 (2), pp.129487. ⟨10.1016/j.jmaa.2025.129487⟩. ⟨hal-04139369⟩
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