135 citations · 273 across the 17 of their papers we have counts for
18 papers
Kinetic models for topological nearest-neighbor interactions
Adrien Blanchet, Pierre Degond
We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consi…
A family of functional inequalities: Lojasiewicz inequalities and displacement convex functions
Jérôme Bolte, Adrien Blanchet
For displacement convex functionals in the probability space equip\-ped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Łoja\-si…
Computation of Cournot-Nash equilibria by entropic regularization
Adrien Blanchet, Guillaume Carlier, Luca Nenna
We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7…
Topological interactions in a Boltzmann-type framework
Adrien Blanchet, Pierre Degond
We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another p…
A hybrid variational principle for the Keller-Segel system in
Adrien Blanchet, José A. Carrillo, David Kinderlehrer +3
We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical v…
Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case
Adrien Blanchet, Guillaume Carlier
This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot-Nash equilibria for ga…