Propagation of chaos for the Burgers equation

Hirofumi OSADA; Shinichi KOTANI

doi:10.2969/jmsj/03720275

Hirofumi OSADA, Shinichi KOTANI

Author information

JOURNAL FREE ACCESS

1985 Volume 37 Issue 2 Pages 275-294

DOI https://doi.org/10.2969/jmsj/03720275

Details

Published: 1985 Received: May 14, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Hirofumi OSADA¹⁾, Shinichi KOTANI²⁾
Right : Hirofumi OSADA¹⁾, Shinichi KOTANI¹⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Mathematics Faculty of Science Kyoto University
2) Department of Mathematics Faculty of Science Kyoto University

Right :
1) Department of Mathematics Faculty of Science Kyoto University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D. G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc., 73(1968), 890-896.
2) D. G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal., 25 (1967), 81-122.
3) P. Calderoni and M. Pulvirenti, Propagation of chaos for Burgers equation, Ann. Inst. H. Poincaré, Sect. A Physique Théorique, 39 (1983), 85-97.
4) E. Gutkin and M. Kac, Propagation of chaos and the Burgers equation, SIAM J. Appl. Math., 43 (1983), 971-980.
5) H. P. McKean, Propagation of chaos for a class of nonlinear parabolic equation, Lecture series in differential equations, Session 7: Catholic Univ., 1967.
6) J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), 931-954.
7) H. Osada, Moment estimates for parabolic equations in the divergence form, to appear in J. Math. Kyoto Univ.
8) A. S. Sznitman, Nonlinear reflecting diffusion process and the propagation of chaos and fluctuations associated, J. Func. Anal., 56 (1984), 311-339.
9) H. Tanaka, Some probabilistic problems in the spatially homogeneous Boltzmann equation, Proc. of IFIP-ISI conf. on theory and applications of random fields, Bangalore, 1982.

Right : [1] D. G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc., 73 (1968), 890-896.
[2] D. G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal., 25 (1967), 81-122.
[3] P. Calderoni and M. Pulvirenti, Propagation of chaos for Burgers equation, Ann. Inst. H. Poincaré, Sect. A Physique Théorique, 39 (1983), 85-97.
[4] E. Gutkin and M. Kac, Propagation of chaos and the Burgers equation, SIAM J. Appl. Math., 43 (1983), 971-980.
[5] H. P. McKean, Propagation of chaos for a class of nonlinear parabolic equation, Lecture series in differential equations, Session 7: Catholic Univ., 1967.
[6] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), 931-954.
[7] H. Osada, Moment estimates for parabolic equations in the divergence form, to appear in J. Math. Kyoto Univ.
[8] A. S. Sznitman, Nonlinear reflecting diffusion process and the propagation of chaos and fluctuations associated, J. Func. Anal., 56 (1984), 311-339.
[9] H. Tanaka, Some probabilistic problems in the spatially homogeneous Boltzmann equation, Proc. of IFIP-ISI conf. on theory and applications of random fields, Bangalore, 1982.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!