Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1

Li Ta-Tsien

Séminaire Équations aux dérivées partielles (Polytechnique) (1979-1980)

  • page 1-21

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Ta-Tsien, Li. "Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1." Séminaire Équations aux dérivées partielles (Polytechnique) (1979-1980): 1-21. <http://eudml.org/doc/111758>.

@article{Ta1979-1980,
author = {Ta-Tsien, Li},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {discontinuous initial condition; Cauchy problem; boundary value problem; first order hyperbolic system; quasilinear problem; regularity},
language = {fre},
pages = {1-21},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1},
url = {http://eudml.org/doc/111758},
year = {1979-1980},
}

TY - JOUR
AU - Ta-Tsien, Li
TI - Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1979-1980
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 21
LA - fre
KW - discontinuous initial condition; Cauchy problem; boundary value problem; first order hyperbolic system; quasilinear problem; regularity
UR - http://eudml.org/doc/111758
ER -

References

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  1. [1] J. Schauder: Cauchy'sches problem für partielle differentialgleichungen erste Ordnung, Commentarii Math., Helvetici, 9, 1937, p.263-283. JFM63.0441.01
  2. [2] K.O. Friedrichs: Nonlinear hyperbolic differential equations of two independent variables, Amer. Jour. of Math., 70, 1948, p.555-589. Zbl0039.10601MR25659
  3. [3] R. Courant, P.D. Lax: On nonlinear differential equations with two independent variables. Comm. Pure Appl. Math., 2, 1949, p.255-273. Zbl0034.20103MR33443
  4. [4] A. Douglis: Some existence theorems for hyperbolic systems of partial differential equations in two independent variables. Comm. Pure Appl. Math.,2, 1952, p.119-154. Zbl0047.09101MR52666
  5. [5] P. Hartman, A. Wintner: On hyperbolic partial differential equations, Amer. Jour . of Math., 74, 1952, p.834-864. Zbl0048.33302MR51413
  6. [6] R. Courant, E. Isaacson, M. Rees: On the solution of nonlinear hyperbolic differential equations by finite difference, Comm. Pure Appl. Math., 5, 1952, p.243-255. Zbl0047.11704MR53336
  7. [7] P.D. Lax: Nonlinear hyperbolic equations, Comm. Pure Appl. Math., 6, 1953, p.231-258. Zbl0050.31705MR56176
  8. [8] P.D. Lax: The initial value problem for nonlinear hyperbolic equations in two independent variables. Ann. Math. Studies, Princeton University Press, 33, 1954, p.211-229. Zbl0057.32502MR68093
  9. [9] R. Courant, P.D. Lax: Cauchy's problem for nonlinear hyperbolic equations in two independent variables. Annali di Matematica pura ed Applicata, 40, 1955, p.161-166. Zbl0065.32901MR76161
  10. [10] R. Courant: Cauchy's problem for hyperbolic quasi-linear systems of first order partial differential equations in two independent variables. Comm. Pure Appl. Math., 14, 1961, p.257-265. Zbl0102.31202MR131670
  11. [11] Li Ta- tsien, Yu Wen-tzu: Cauchy's problem for quasi-linear hyperbolic systems of first order partial differential equations. Math. Progress, 7, 1964, p.152-171. MR232091
  12. [12] P.D. Lax: Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys., 5, 1964, p.611-613. Zbl0135.15101MR165243
  13. [13] J.B. Keller, L. Ting: Periodic vibrations of systems governed by nonlinear partial differential equations", Comm. Pure Appl. Math., 19, 1966, p.371-420. Zbl0284.35004MR205520
  14. [14] T. Nishida: Nonlinear hyperbolic equations and related topics in fluid dynamics. Publications Mathématiquesd'Orsay, 1978, 02. Zbl0392.76065MR481578
  15. [15] A. Jeffrey: Quasilinear hyperbolic systems and waves. Research Notes in Mathematics, Pitman Publishing, 1976. Zbl0322.35060MR417585
  16. [16] F. John: Formation of singularities in one-dimensional nonlinear wave propagation. Comm. Pure Appl. Math., 27, 1974, p.377-465. Zbl0302.35064MR369934
  17. [17] R. Courant, K.O. Friedrichs: Supersonic flow and shock waves. New York, 1948. Zbl0041.11302MR29615
  18. [18] P. Giovanni: Sulla risonluzione del problema misto per le equazioni iperboliche non lineari mediante le differenze finite. Ann. Mat. Pura. Appl., 46, 1958, p.313-341. Zbl0090.07302MR123851
  19. [19] V. Thomée: Difference methods for two dimensional mixed problems for hyperbolic first order systems. Arch. Rat. Mech. Anal., 8, 1961, p.68-88. Zbl0104.32202MR129555
  20. [20] V. Thomée: A mixed boundary-value problem for hyperbolic first-order systems with derivatives in the boundary conditions. Arch. Rat. Mech.Anal., 8, 1961, p.433-443. Zbl0104.32203MR145212
  21. [21] B.L. Rozdestvenskii, N.N. Yanenko: Systems of quasilinear equations. Izd. NaukaMoskva, 1968. 
  22. [22] Li Ta-tsien, Yu Wen-tzu: Some existence theorems for quasi-linear hyperbolic systems of partial differential equations in two independent variables, (I) Typical boundary value problems, Scientia Sinica,13, n°4, 1964, p.529-549. Zbl0173.12305MR176229
  23. [23] Li Ta-tsien, Yu Wen-tzu: (II) Typical boundary value problems of functional form and typical free boundary problems, ibid.13, n°4, 1964, p.551-562. Zbl0173.12305MR176230
  24. [24] Li Ta-tsien, Yu Wen-tzu: (III) General boundary value problems and general free boundary problems, ibid, 14, n°7, 1965, p.1065-1067; Bulletin de Fudan, 10, n° 2-3, 1965, p.113-128. Zbl0173.12305MR183960
  25. [25] Gu Chao-hao, Li Ta-tsien et coll.: Ecoulements plans supersoniques autour d'une arête avec une frontière courbe. Recueil de la Faculté de Mathématiques de l'UniversitéFudan, 1960, p.17-28. 
  26. [26] Gu Chao-hao: Une méthode pour résoudre le problème de l'écoulement supersonique autour d'une arête avec une frontière courbe. Bulletin deFudan, 7, n°1, 1962, p.11-14. 
  27. [27] Gu Chao-hao: A boundary value problem for hyperbolic systems and its applications. Acta Math. Sinica, 13, 1963, p.32-48. Zbl0161.08301MR163069
  28. [28] D.G. Schaeffer: An application of the Nash-Moser theorem to a free boundary problem. Lecture Notes in Mathematics, 648, 1978, p.129-143. Zbl0393.35066MR499455
  29. [29] D.G. Schaeffer: Supersonic flow past a nearly straight wedge. Duke Math. J., 43, 1976, p.637-670. Zbl0356.76046MR413736
  30. [30] Li Ta-tsien: Une remarque sur un problème à frontière libre. C. R. Acad. Sc. Paris, t.289 (9 Juillet 1979), série A, p.99-102. Zbl0423.35086MR549078
  31. [31] Li Ta-tsien: On a free boundary problem. A paraître dans Chinese Annals of Math. 
  32. [32] Li Ta-tsien, Yu Wen-tzu: The local solvability of the boundary value problems for quasi linear hyperbolic systems of partial differential equations. Bulletin deFudan, 2, 1979, p.83-93. 
  33. [33] Gu Chao-hao, Li Ta-tsien et coll.: The Cauchy problem of typical hyperbolic system with discontinuous initial values. Recueil de la Faculté de Mathématiques de l'UniversitéFudan, 1960, p.1-16. 
  34. [34] Gu Chao-hao, Li Ta-tsien, Ho Zon-y: The Cauchy problem of quasi-linear hyperbolic systems with discontinuous initial values (1). Acta Math. Sinica, 11, 1961, p.314-323. Zbl0192.19303
  35. [35] Gu Chao-hao, Li Ta-tsien, Ho Zon-y: (II), ibid, 11, 1961, p.324-327. 
  36. [36] Gu Chao-hao, Li Ta-tsien, Ho Zon-y: (III), ibid, 12, 1962, p.132-143. 
  37. [37] Li Ta-tsien, Yu Wen-tzu: Discontinuous solutions for the quasi-linear hyperbolic systems. A paraître. 
  38. [38] P.D. Lax: Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math., 10, 1957, p.537-566. Zbl0081.08803MR93653
  39. [39] J. Glimm: Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math., 18, 1965, p.697-715. Zbl0141.28902MR194770

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