30 citations · 40 across the 7 of their papers we have counts for
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Revisiting the blow-up criterion and the maximal existence time for solutions of the parabolic-elliptic Keller-Segel system in 2d-Euclidean space
Patrick Maheux, Vittoria Pierfelice
In this paper, we revisit the blow-up criteria for the simplest parabolic-elliptic (PKS) system in the 2D Euclidean space, including a consumption term. In the supercritical mass c…
Upper bounds for the blow-up time of the 2-D parabolic-elliptic Patlak-Keller-Segel model of chemotaxis
Patrick Maheux
In this paper, we obtain upper bounds for the critical time of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment conditio…
The Keller-segel System On The 2d-hyperbolic Space
Patrick Maheux, Vittoria Pierfelice
In this paper, we shall study the parabolic-elliptic Keller-Segel system on the Poincar{é} disk model of the 2D-hyperbolic space. We shall investigate how the negative curvature of…
Log-Sobolev inequalities for semi-direct product operators and applications
Piero D'Ancona, Patrick Maheux, Vittoria Pierfelice
We prove logarithmic Sobolev inequalities for semi-direct product operators (see definition in Section 1). We apply our main results to examples of operators and provide some appli…