Formation of singularities for Hamilton-Jacobi equation with several space variables

Shizuo NAKANE

doi:10.2969/jmsj/04310089

Shizuo NAKANE

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ジャーナルフリー

1991 年 43 巻 1 号 p. 89-100

DOI https://doi.org/10.2969/jmsj/04310089

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Published: 1991 Received: 1989/12/15 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: 引用文献情報訂正内容: Wrong : 1) V. I. Arnold, Mathematical methods of classical mechanics, GTM, Springer, 60, 1978.
2) S. H. Benton, Hamilton-Jacobi equation, A global approach, Academic Press, New York-London, 1977.
3) T. Debeneix, Certains systèmes hyperboliques quasi-linéaires, preprint.
4) A. Douglis, Solutions in the large for multi-dimensional nonlinear equations of first order, Ann. Inst. Fourier, 15 (1965), 1-35.
5) M. Golubitsky and V. Guillemin, Stable mappings and their singularities, GTM, 14, Springer, 1973.
6) S. N. Kruzkov, Generalized solutions of nonlinear first order equations with several independent variables, Math. USSR-Sb., 1 (1967), 93-116.
7) B. Morin, Formes canoniques de singularités dune application différentiable, C. R. Acad. Sci. Paris, 260 (1965), 5662-5665.
8) S. Nakane, Formation of shocks for a single conservation law, SIAM J. Math. Anal., 19 (1988), 1391-1408.
9) D. Schaeffer, A regularity theorem for conservation laws, Adv. in Math., 11 (1973), 358-386.
10) M. Tsuji, Solution globale et propagation des singularités pour l'équation de Hamilton-Jacobi, C. R. Acad. Sci. Paris, 289 (1979), 397-400.
11) M. Tsuji, Formation of singularities for Hamilton-Jacobi equation I, Proc. Japan Acad., 59 (1983), 55-58.
12) M. Tsuji, Formation of singularities for Hamilton-Jacobi equation II, J. Math. Kyoto Univ., 26 (1986), 299-308.
13) H. Whitney, On singularities of mappings of Euclidean spaces I, Ann. of Math., 62 (1955), 374-410

Right : [1] V. I. Arnold, Mathematical methods of classical mechanics, GTM, Springer, 60, 1978.
[2] S. H. Benton, Hamilton-Jacobi equation, A global approach, Academic Press, New York-London, 1977.
[3] T. Debeneix, Certains systèmes hyperboliques quasi-linéaires, preprint.
[4] A. Douglis, Solutions in the large for multi-dimensional nonlinear equations of first order, Ann. Inst. Fourier, 15 (1965), 1-35.
[5] M. Golubitsky and V. Guillemin, Stable mappings and their singularities, GTM, 14, Springer, 1973.
[6] S. N. Kruzkov, Generalized solutions of nonlinear first order equations with several independent variables, Math. USSR-Sb., 1 (1967), 93-116.
[7] B. Morin, Formes canoniques de singularités dune application différentiable, C. R. Acad. Sci. Paris, 260 (1965), 5662-5665.
[8] S. Nakane, Formation of shocks for a single conservation law, SIAM J. Math. Anal., 19 (1988), 1391-1408.
[9] D. Schaeffer, A regularity theorem for conservation laws, Adv. in Math., 11 (1973), 358-386.
[10] M. Tsuji, Solution globale et propagation des singularités pour l'équation de Hamilton-Jacobi, C. R. Acad. Sci. Paris, 289 (1979), 397-400.
[11] M. Tsuji, Formation of singularities for Hamilton-Jacobi equation I, Proc. Japan Acad., 59 (1983), 55-58.
[12] M. Tsuji, Formation of singularities for Hamilton-Jacobi equation II, J. Math. Kyoto Univ., 26 (1986), 299-308.
[13] H. Whitney, On singularities of mappings of Euclidean spaces I, Ann. of Math., 62 (1955), 374-410

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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