Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

By José Antonio Carrillo, Robert J. McCann, Cédric Villani. 2003

580 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6b03edbafb6a753401453131b4009ad36e4e0e36

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In Applied Mathematics

Citations in the corpus

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, unknown): “[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.”
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.”
Sharp logarithmic Sobolev inequalities on gradient solitons and applications (2008, methodology): “The HWI inequalities were originally introduced in [33] and used in other models in nonlinear PDEs in [6].”
Chapter 1 – Gradient Flows of Probability Measures (2007, background): “5 Drift diffusion equations with non local terms Let us consider, as in [28, 29], a functional φ which is the sum of internal, potential, and interaction energy: φ(μ) := ∫”
Dimensionality of Local Minimizers of the Interaction Energy (2012, background): “Let us finally mention that the gradient flow of the energy EW in the Wasserstein sense d2 [12, 1, 13] has been extensively studied in recent years [24, 7, 5, 6, 8, 11, 10, 9, 17, 18, 30, 3, 2].”
Convergence to equilibrium for granular media equations and their Euler schemes (2003, methodology): “This result is quite classical but we reproduce its proof in order to give an idea of the strategy used in [7].”
Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, methodology): “Both the PDE approach in [9] and the approach based on synchronuous coupling in [11, 42] require global positive curvature bounds.”
Hypocoercive Diffusion Operators (2006, background): “Among a large literature, I shall only quote some of my own works: entropy production estimates for the spatially homogeneous Boltzmann equation, in collaboration with Giuseppe Toscani [25], [26], [28]; and for certain nonlinear diffusion equations with a convex mean-field interaction, in collaborat”
Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus (2018, background): “Systems of interacting particles arise in a myriad of applications ranging from opinion dynamics [41], granular materials [6,11,25] and mathematical biology [8,47] to statistical mechanics [50], galactic dynamics [18], droplet growth [29], plasma physics [14], and synchronisation [48].”
Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued Initial Data (2012, unknown): “Drawing intuition from classical Bakry–Emery analysis and the more recent insights of entropy dissipation methods (see for example [1,20,21]) it is expected that the convexity and coercivity of F̃ are equivalent to the decay estimate (A.”
Long-Time Asymptotics of Kinetic Models of Granular Flows (2004, methodology): “The proof in [ 9 ] follows along the lines of the recent paper by Otto [20], where the Wasserstein metric first entered as a main ingredient into the study of the long‐time behavior of nonlinear diusion equations.”
Existence, Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in $${\mathbb{R}^2}$$R2 with Measure-Valued Initial Data (2012, background): “[1, 20, 21]) it is expected that convexity and coercivity of F̃ are equivalent to the decay estimate (A.”
Phi-entropy inequalities for diffusion semigroups (2008, background): “For ρ > 0, solutions ut to (48) have been shown to converge to a unique equilibrium u∞ as t goes to infinity (see [CMV03] for instance).”
Equilibria of homogeneous functionals in the fair-competition regime (2016, background): “The strong connection between the functional Fm,k and the PDE (1.2) is due to the fact that the functional Fm,k is non-increasing along the trajectories of the system.”
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (2011, methodology): “This review is dedicated to the parabolic-elliptic Patlak-Keller-Segel model and tries to describe the progress made through energy and functional inequalities methods in the idea of [64, 1, 21].”