Propagation of chaos for the Burgers equation

Hirofumi OSADA; Shinichi KOTANI

doi:10.2969/jmsj/03720275

Hirofumi OSADA, Shinichi KOTANI

著者情報

ジャーナルフリー

1985 年 37 巻 2 号 p. 275-294

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

詳細

Published: 1985 Received: 1984/05/14 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Hirofumi OSADA¹⁾, Shinichi KOTANI²⁾
Right : Hirofumi OSADA¹⁾, Shinichi KOTANI¹⁾

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Department of Mathematics Faculty of Science Kyoto University
2) Department of Mathematics Faculty of Science Kyoto University

訂正後 :
1) Department of Mathematics Faculty of Science Kyoto University

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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