Prolongation of classical solutions and singularities of generalized solutions

Mikio Tsuji

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 6, page 505-523
  • ISSN: 0294-1449

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Tsuji, Mikio. "Prolongation of classical solutions and singularities of generalized solutions." Annales de l'I.H.P. Analyse non linéaire 7.6 (1990): 505-523. <http://eudml.org/doc/78237>.

@article{Tsuji1990,
author = {Tsuji, Mikio},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {global classical solutions; formation of singularities; Cauchy problems; Rankin-Hugoniot's condition},
language = {eng},
number = {6},
pages = {505-523},
publisher = {Gauthier-Villars},
title = {Prolongation of classical solutions and singularities of generalized solutions},
url = {http://eudml.org/doc/78237},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Tsuji, Mikio
TI - Prolongation of classical solutions and singularities of generalized solutions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 6
SP - 505
EP - 523
LA - eng
KW - global classical solutions; formation of singularities; Cauchy problems; Rankin-Hugoniot's condition
UR - http://eudml.org/doc/78237
ER -

References

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  1. [1] S. Benton, Hamilton-Jacobi equation, A global approach, Academic Press, 1977. Zbl0418.49001MR442431
  2. [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. Zbl0543.35011MR732102
  3. [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. [4] B. Gaveau, Asymptotic behavior of shocks for single conservation law in two space dimensions, preprint. 
  5. [5] A. Haar, Sur l'unicité des solutions des équations aux dérivées partielles, C. R. Acad. Sci. Paris, t. 187, 1928, pp. 23-26. Zbl54.0496.01JFM54.0496.01
  6. [6] J. Guckenheimer, Solving a single conservation law, Lect. Notes Math., Vol. 468, 1975, pp. 108-134 (Springer-Verlag). Zbl0306.35020MR606765
  7. [7] G. Jennings, Piecewise smooth solutions of single conservation law exists, Adv. Math., Vol. 33, 1979, pp. 192-205. Zbl0418.35021MR544849
  8. [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. Zbl0268.35062MR350216
  9. [9] P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Res. Notes Math., Vol. 69, Pitman, 1982. Zbl0497.35001MR667669
  10. [10] S. Nakane, Formation of shocks for a single conservation law, S.I.A.M. J. Math. Anal., Vol. 19, 1988, pp. 1391-1408. Zbl0681.35057MR965259
  11. [11] B. Rozdestvenskii, Discontinuous solutions of hyperbolic systems of quasi-linear equations, Russ. Math. Surveys, Vol. 15, 1960, pp. 53-111. Zbl0098.29504MR136865
  12. [12] D.G. Schaeffer, A regularity theorem for conservation law, Adv. Math., Vol. 11, 1973, pp. 358-386. Zbl0267.35009MR326178
  13. [13] M. Tsuji, Formation of singularities for Hamilton-Jacobi equation II, J. Math. Kyoto Univ., Vol. 26, 1986, pp. 299-308. Zbl0655.35009MR849221
  14. [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. Zbl0594.35052MR812339
  15. [15] M. Tsuji and Li Ta-TsienRemarks on characteristics of partial differential equations of first order, Funkcial. Ekvac., Vol. 32, 1989, pp. 157-162. Zbl0694.35026MR1006093
  16. [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. Zbl0008.15802
  17. [17] H. Whitney, On singularities of mappings of Euclidean spaces I. Ann. Math., Vol. 62, 1955, pp. 374-410. Zbl0068.37101MR73980

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