30 citations · 40 across the 7 of their papers we have counts for
8 papers
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…
Super-Poincaré and Nash-type inequalities for Subordinated Semigroups
Ivan Gentil, Patrick Maheux
We prove that if a super-Poincaré inequality is satisfied by an infinitesimal generator of a symmetric contracting semigroup then it implies a corresponding super-Poincaré ine…
Weighted Nash Inequalities
Dominique Bakry, François Bolley, Ivan Gentil +1
Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we pres…
New Proofs of Davies-Simon's Theorems about Ultracontractivity and Logarithmic Sobolev Inequalities related to Nash Type Inequalities
Patrick Maheux
We present new proofs of two theorems of E.B. Davies and B. Simon about ultracontractivity property for of semigroups of operators and logarithmic Sobolev inequalities with paramet…
Nash type inequalities for fractional powers of non-negative self-adjoint operators
Alexander Bendikov, Patrick Maheux
Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator , we prove a Nash type inequality for the fractional powers of . Under some as…