Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media

By José Antonio Carrillo, Robert J. McCann, Cédric Villani. 2006

388 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/1b0a90bff5b70d53112896f909e714b1f7deb72d

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In Applied Mathematics

In Geometry and Topology

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model (2010, background): “1) if the transport term v · ∇xf is dropped [9, 10].”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, background): “This basic intuitive idea, introduced in [37] for the porous medium equation and generalized to a wide class of equations in [19], was made completely rigorous for a large class of equations in [2] [3] including some particular instances of (1.2).”
Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces (2009, background): “This point of view was further developed in [5] and [12].”
Asymptotic Estimates for the Parabolic-Elliptic Keller-Segel Model in the Plane (2012, background): “For completeness, let us mention that results of exponential convergence for problems with mean field have been obtained earlier in [15, 16], but only for interaction potentials involving much smoother kernels than G2.”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, neutral): “For subsequent developments in this direction, see works of Ambrosio, CorderoErausquin, Carrillo, Figalli, Gigli, Lott, Maggi, McCann, Nazaret, Otto, Pratelli, von Renesse, Schmuckenschläger, Sturm, Topping and Villani in [95] [110] [30] [31] [32] [5] [24] [116] [127] [88] [87] [99] [52].”
Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions (2008, background): “4) can formally be considered a particular instance of the general family of PDEs studied in [8, 1, 9].”
Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations (2007, background): “This principle was applied in other simplified granular media models as in [7, 8, 43, 44] with success.”
Dimensionality of Local Minimizers of the Interaction Energy (2012, background): “To prove Theorem 2, we need some convex analysis concepts, see [13, 1] and the references therein.”
The derivation of swarming models: Mean-field limit and Wasserstein distances (2013, methodology): “The idea is similar to the evolution of the euclidean Wassertein distance in [30, 31, 70].”
Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, neutral): “[9] Carrillo, J. A., McCann, R. J., and Villani, C. Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.”
A Family of Nonlinear Fourth Order Equations of Gradient Flow Type (2009, background): “[12] Carrillo, J. A.; McCann, R. J. and Villani, C. Contractions in the 2-Wasserstein length space and thermalization of granular media.”