Prolongation of classical solutions and singularities of generalized solutions
Tsuji, Mikio
Annales de l'I.H.P. Analyse non linéaire, Tome 7 (1990), p. 505-523 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1990-01-01
@article{AIHPC_1990__7_6_505_0,
     author = {Tsuji, Mikio},
     title = {Prolongation of classical solutions and singularities of generalized solutions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {7},
     year = {1990},
     pages = {505-523},
     mrnumber = {1079570},
     zbl = {0722.35025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1990__7_6_505_0}
}

Tsuji, Mikio. Prolongation of classical solutions and singularities of generalized solutions. Annales de l'I.H.P. Analyse non linéaire, Tome 7 (1990) pp. 505-523. http://gdmltest.u-ga.fr/item/AIHPC_1990__7_6_505_0/

[1] S. Benton, Hamilton-Jacobi equation, A global approach, Academic Press, 1977. | MR 442431 | Zbl 0418.49001

[2] M.G. Crandall, L.C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. A.M.S., Vol. 282, 1984, pp. 487-502. | MR 732102 | Zbl 0543.35011

[3] B. Doubnov, Sur l'existence globale des solutions des équations d'Hamilton, Supplément dans "Théorie des perturbations et méthodes asymptotiques" par V. P. MASLOV (traduction française), Dunod, 1972.

[4] B. Gaveau, Asymptotic behavior of shocks for single conservation law in two space dimensions, preprint.

[5] A. Haar, Sur l'unicité des solutions des équations aux dérivées partielles, C. R. Acad. Sci. Paris, t. 187, 1928, pp. 23-26. | JFM 54.0496.01

[6] J. Guckenheimer, Solving a single conservation law, Lect. Notes Math., Vol. 468, 1975, pp. 108-134 (Springer-Verlag). | MR 606765 | Zbl 0306.35020

[7] G. Jennings, Piecewise smooth solutions of single conservation law exists, Adv. Math., Vol. 33, 1979, pp. 192-205. | MR 544849 | Zbl 0418.35021

[8] P.D. Lax, Hyperbolic systems of conservation law and the methematical theory of shock waves, S.I.A.M. Regional Conference Ser. Appl. Math., Vol. 11, 1973. | MR 350216 | Zbl 0268.35062

[9] P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Res. Notes Math., Vol. 69, Pitman, 1982. | MR 667669 | Zbl 0497.35001

[10] S. Nakane, Formation of shocks for a single conservation law, S.I.A.M. J. Math. Anal., Vol. 19, 1988, pp. 1391-1408. | MR 965259 | Zbl 0681.35057

[11] B. Rozdestvenskii, Discontinuous solutions of hyperbolic systems of quasi-linear equations, Russ. Math. Surveys, Vol. 15, 1960, pp. 53-111. | MR 136865 | Zbl 0098.29504

[12] D.G. Schaeffer, A regularity theorem for conservation law, Adv. Math., Vol. 11, 1973, pp. 358-386. | MR 326178 | Zbl 0267.35009

[13] M. Tsuji, Formation of singularities for Hamilton-Jacobi equation II, J. Math. Kyoto Univ., Vol. 26, 1986, pp. 299-308. | MR 849221 | Zbl 0655.35009

[14] M. Tsuji and Li Ta-Tsien, Globally classical solutions for nonlinear equations of first order, Comm. Partial Diff. Eq., Vol. 10, 1985, pp. 1451-1463. | MR 812339 | Zbl 0594.35052

[15] M. Tsuji andLi Ta-TsienRemarks on characteristics of partial differential equations of first order, Funkcial. Ekvac., Vol. 32, 1989, pp. 157-162. | MR 1006093 | Zbl 0694.35026

[16] T. Wazewski, Sur l'unicité et la limitation des intégrales des équations aux dérivées partielles du premier ordre, Rend. Acc. Lincei, Vol. 17, 1933, pp. 372-376. | Zbl 0008.15802

[17] H. Whitney, On singularities of mappings of Euclidean spaces I. Ann. Math., Vol. 62, 1955, pp. 374-410. | MR 73980 | Zbl 0068.37101