Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems, Mathematics of Computation, vol.73, issue.245, pp.63-94, 2004. ,
DOI : 10.1090/S0025-5718-03-01549-7
URL : https://hal.archives-ouvertes.fr/hal-00387865
How Nature Works: The science of Self-Organized Criticality, 1986. ,
Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case, Probability Theory and Related Fields, vol.34, issue.6 ,
DOI : 10.1007/s00440-010-0291-x
URL : https://hal.archives-ouvertes.fr/inria-00410248
On some unsteady motions of a liquid and gas in a porous medium, Akad. Nauk SSSR. Prikl. Mat. Meh, vol.16, pp.67-78, 1952. ,
Processus associésassociés`associésà l'´ equation des milieux poreux, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.23, issue.4, pp.793-832, 1996. ,
A semilinear equation in L 1 (R N ), Ann. Scuola Norm, Sup. Pisa Cl. Sci, vol.2, issue.4, pp.523-555, 1975. ,
The continuous dependence on ? of solutions of u t ? ??(u) = 0, Indiana Univ, Math. J, vol.30, pp.161-177, 1981. ,
A numerical method for solving the problem u t ? ?f (u) = 0, RAIRO Anal, Numér, vol.13, pp.297-312, 1979. ,
Probabilistic representation for solutions of an irregular porous media type equation, The Annals of Probability, vol.38, issue.5, pp.1870-1900, 2010. ,
DOI : 10.1214/10-AOP526
URL : https://hal.archives-ouvertes.fr/hal-00279975
A stochastic particle method for some one-dimensional nonlinear p.d.e., Mathematics and Computers in Simulation, vol.38, issue.1-3, pp.43-50, 1995. ,
DOI : 10.1016/0378-4754(93)E0065-D
Diffusive BGK approximations for nonlinear multidimensional parabolic equations, Indiana University Mathematics Journal, vol.49, issue.2, pp.723-749, 2000. ,
DOI : 10.1512/iumj.2000.49.1811
An alternative method of cross-validation for the smoothing of density estimates, Biometrika, vol.71, issue.2, pp.353-360, 1984. ,
DOI : 10.1093/biomet/71.2.353
Uniqueness of solutions of the initial-value problem for u t ? ??(u) = 0, J. Math. Pures Appl, vol.58, issue.9, pp.153-163, 1979. ,
Local Rigidity and Self-Organized Criticality for Avalanches, Europhysics Letters (EPL), vol.29, issue.2, pp.111-116, 1995. ,
DOI : 10.1209/0295-5075/29/2/001
Propagation of chaos for Burgers' equation, Ann. Inst. H. Poincaré Sect. A (N.S.), vol.39, pp.85-97, 1983. ,
High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems, SIAM Journal on Numerical Analysis, vol.45, issue.5, pp.2098-2119, 2007. ,
DOI : 10.1137/060664872
Implementing Kernel Density Estimation on GPU: application to a probabilistic algorithm for PDEs of porous media type ,
Particle simulation of plasmas, Rev. Modern Phys, pp.403-447, 1983. ,
Convergence to the viscous porous medium equation and propagation of chaos, ALEA Lat, Am. J. Probab. Math. Stat, vol.4, pp.185-203, 2008. ,
Solving ordinary differential equations. I, second ed, Series in Computational Mathematics, 1993. ,
Uniformly High-Order Accurate Nonoscillatory Schemes. I, SIAM Journal on Numerical Analysis, vol.24, issue.2, pp.279-309, 1987. ,
DOI : 10.1137/0724022
Computer simulation using particles, 1981. ,
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms, Journal of Computational Physics, vol.126, issue.2, pp.449-467, 1996. ,
DOI : 10.1006/jcph.1996.0149
The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-276, 1995. ,
DOI : 10.1002/cpa.3160480303
A Brief Survey of Bandwidth Selection for Density Estimation, Journal of the American Statistical Association, vol.53, issue.433, pp.91-401, 1996. ,
DOI : 10.1214/aoms/1177696810
Probabilistic approximation for a porous medium equation, Stochastic Process, Appl, vol.89, pp.81-99, 2000. ,
Propagation of chaos and fluctuations for a moderate model with smooth initial data, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.34, issue.6, pp.727-766, 1998. ,
DOI : 10.1016/S0246-0203(99)80002-8
Solution of Nonlinear Diffusion Problems by Linear Approximation Schemes, SIAM Journal on Numerical Analysis, vol.30, issue.6, pp.1703-1722, 1993. ,
DOI : 10.1137/0730087
Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1991. ,
Propagation of chaos for a class of non-linear parabolic equations., Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, Catholic Univ, Air Force Office Sci. Res, pp.41-57, 1967. ,
A propagation of chaos result for a system of particles with moderate interaction, Stochastic Process, Appl, vol.26, pp.317-332, 1987. ,
A law of large numbers for moderately interacting diffusion processes A fluctuation theorem for moderately interacting diffusion processes Simulation of the solution of a viscous porous medium equation by a particle method, Z. Wahrsch. Verw. Gebiete Probab. Theory Related Fields SIAM J. Numer. Anal, vol.69, issue.35, pp.279-322, 1985. ,
Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput, vol.25, pp.129-155, 2005. ,
On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962. ,
DOI : 10.1214/aoms/1177704472
Interacting diffusions approximating the porous medium equation and propagation of chaos, Stochastic Process, Appl, vol.117, pp.526-538, 2007. ,
A numerical approach to degenerate parabolic equations, Numerische Mathematik, vol.92, issue.2, pp.357-381, 2002. ,
DOI : 10.1007/s002110100330
Empirical choice of histograms and kernel density estimators, Scand, J. Statist, vol.9, pp.65-78, 1982. ,
Biased and Unbiased Cross-Validation in Density Estimation, Journal of the American Statistical Association, vol.9, issue.400, pp.1131-1146, 1987. ,
DOI : 10.1214/aoms/1177696810
A reliable data-based bandwidth selection method for kernel density estimation, J. Roy. Statist. Soc. Ser. B, vol.53, pp.683-690, 1991. ,
Monotone operators in Banach space and nonlinear partial differential equations, Mathematical Surveys and Monographs 49, 1997. ,
Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advanced numerical approximation of nonlinear hyperbolic equations (Cetraro, Lecture Notes in Math. 1697, pp.325-432, 1997. ,
Density estimation for statistics and data analysis, Monographs on Statistics and Applied Probability, 1986. ,
Multidimensional diffusion processes, Classics in Mathematics, 2006. ,
DOI : 10.1007/3-540-28999-2
Topics in propagation of chaos, Lecture Notes in Math, vol.22, issue.1, pp.165-251, 1991. ,
DOI : 10.1070/SM1974v022n01ABEH001689
The Maximal Smoothing Principle in Density Estimation, Journal of the American Statistical Association, vol.9, issue.410, pp.470-477, 1990. ,
DOI : 10.1080/01621459.1985.10477163
Oversmoothed Nonparametric Density Estimates, Journal of the American Statistical Association, vol.21, issue.389, pp.209-214, 1985. ,
DOI : 10.1214/aos/1176345341
Kernel smoothing, Monographs on Statistics and Applied Probability 60, 1995. ,
On Choosing a Delta-Sequence, The Annals of Mathematical Statistics, vol.41, issue.5, pp.1665-1671, 1970. ,
DOI : 10.1214/aoms/1177696810
Kernel density estimation via diffusion, Submitted to the Annals of statistics, 2007. ,
Université Paris 13, 99, avenue Jean-Baptiste Clément, F-93430 Villetaneuse and ENSTA ParisTech, Géométrie et Applications (LAGA), vol.32 ,
Boulevard Victor , F-75739 Paris Cedex 15, INRIA Rocquencourt and Cermics Ecole des Ponts et Chaussées, Projet MATHFI Domaine de Voluceau, BP 105 F-78153 Le Chesnay Cedex ,