119 citations · 148 across the 8 of their papers we have counts for
8 papers
Generalized solutions of a kinetic granular media equation by a gradient flow approach
Martial Agueh, Guillaume Carlier
We consider a one-dimensional kinetic model of granular media in the case where the interaction potential is quadratic. Taking advan- tage of a simple first integral, we can use a…
A dual Moser-Onofri inequality and its extensions to higher dimensional spheres
Martial Agueh, Shirin Boroushaki, Nassif Ghoussoub
We use optimal mass transport to provide a new proof and a dual formula to the Moser-Onofri inequality on $\s^2$ in the same spirit as the approach of Cordero-Erausquin, Nazaret an…
Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system
Reinel Sospedra-Alfonso, Martial Agueh
We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by…
Global Classical Solutions of the Relativistic Vlasov-Darwin System with Small Cauchy Data: the Generalized Variables Approach
Reinel Sospedra-Alfonso, Martial Agueh, Reinhard Illner
We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed i…
An efficient numerical algorithm for the L2 optimal transport problem with applications to image processing
Louis-Philippe Saumier, Martial Agueh, Boualem Khouider
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is ba…
Large time asymptotics of the doubly nonlinear equation in the non-displacement convexity regime
Martial Agueh, Adrien Blanchet, José Antonio Carrillo
We study the long-time asymptotics of the doubly nonlinear diffusion equation in $\RR^n$, in the range $\frac{n-p}{n(p-1)}<m>\frac{n-p+1}{…