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Publications Influence

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

- J. Carrillo, R. McCann, C. Villani
- Mathematics
- 31 December 2003

The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4]… Expand

395 33

Asymptotic L1-decay of solutions of the porous medium equation to self-similarity

- J. Carrillo, G. Toscani
- Mathematics
- 2000

We consider the flow of gas in an N-dimensional porous medium with initial density v0NxO 0. The density vNx;tO then satisfies the nonlinear degenerate parabolic equa- tion vt E —v m where m> 1 is a… Expand

263 25- PDF

On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions

- A. Bobylev, J. Carrillo, I. Gamba
- Physics
- 1 February 2000

We investigate a Boltzmann equation for inelastic scattering in which the relative velocity in the collision frequency is approximated by the thermal speed. The inelasticity is given by a velocity… Expand

215 19

Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities

- J. Carrillo, A. Jüngel, P. Markowich, G. Toscani, A. Unterreiter
- Mathematics
- 1 May 2001

Abstract. We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with confinement by a uniformly convex potential, 2)… Expand

307 17- PDF

Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

- María J. Cáceres, J. Carrillo, B. Perthame
- Mathematics, Medicine
- Journal of mathematical neuroscience
- 22 October 2010

TLDR

81 15- PDF

Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

- J. Carrillo, G. Toscani
- Mathematics
- 1 February 2002

Abstract: In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation ut=−(uuxxx)x, modeling the evolution of the… Expand

101 15- PDF

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

- J. Carrillo, R. McCann, C. Villani
- Mathematics
- 1 February 2006

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles… Expand

299 14- PDF

Particle, kinetic, and hydrodynamic models of swarming

- J. Carrillo, M. Fornasier, G. Toscani, F. Vecil
- Physics
- 2010

We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with… Expand

244 13- PDF

Infinite time aggregation for the critical Patlak-Keller-Segel model in ℝ2

- A. Blanchet, J. Carrillo, N. Masmoudi
- Mathematics
- 30 October 2007

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we… Expand

205 13- PDF

Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model

- J. Carrillo, M. Fornasier, J. Rosado, G. Toscani
- Computer Science, Mathematics
- SIAM J. Math. Anal.
- 26 February 2010

TLDR

319 11- PDF

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