Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1979-1980), Exposé no. 23, 21 p.
@article{SEDP_1979-1980____A24_0,
     author = {Ta-Tsien, Li},
     title = {Probl\`emes aux limites et solutions discontinues pour les syst\`emes hyperboliques quasi lin\'eaires d'ordre 1},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:23},
     pages = {1--21},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1979-1980},
     zbl = {0468.35063},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_1979-1980____A24_0/}
}
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) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:23
PY  - 1979-1980
SP  - 1
EP  - 21
PB  - Ecole Polytechnique, Centre de Mathématiques
UR  - http://www.numdam.org/item/SEDP_1979-1980____A24_0/
LA  - fr
ID  - SEDP_1979-1980____A24_0
ER  - 
%0 Journal Article
%A Ta-Tsien, Li
%T Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:23
%D 1979-1980
%P 1-21
%I Ecole Polytechnique, Centre de Mathématiques
%U http://www.numdam.org/item/SEDP_1979-1980____A24_0/
%G fr
%F SEDP_1979-1980____A24_0
Ta-Tsien, Li. Problèmes aux limites et solutions discontinues pour les systèmes hyperboliques quasi linéaires d'ordre 1. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1979-1980), Exposé no. 23, 21 p. http://www.numdam.org/item/SEDP_1979-1980____A24_0/

[1] J. Schauder: Cauchy'sches problem für partielle differentialgleichungen erste Ordnung, Commentarii Math., Helvetici, 9, 1937, p.263-283. | JFM

[2] K.O. Friedrichs: Nonlinear hyperbolic differential equations of two independent variables, Amer. Jour. of Math., 70, 1948, p.555-589. | MR | Zbl

[3] R. Courant, P.D. Lax: On nonlinear differential equations with two independent variables. Comm. Pure Appl. Math., 2, 1949, p.255-273. | MR | Zbl

[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. | MR | Zbl

[5] P. Hartman, A. Wintner: On hyperbolic partial differential equations, Amer. Jour . of Math., 74, 1952, p.834-864. | MR | Zbl

[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. | MR | Zbl

[7] P.D. Lax: Nonlinear hyperbolic equations, Comm. Pure Appl. Math., 6, 1953, p.231-258. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR

[12] P.D. Lax: Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys., 5, 1964, p.611-613. | MR | Zbl

[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. | MR | Zbl

[14] T. Nishida: Nonlinear hyperbolic equations and related topics in fluid dynamics. Publications Mathématiques d'Orsay, 1978, 02. | MR | Zbl

[15] A. Jeffrey: Quasilinear hyperbolic systems and waves. Research Notes in Mathematics, Pitman Publishing, 1976. | MR | Zbl

[16] F. John: Formation of singularities in one-dimensional nonlinear wave propagation. Comm. Pure Appl. Math., 27, 1974, p.377-465. | MR | Zbl

[17] R. Courant, K.O. Friedrichs: Supersonic flow and shock waves. New York, 1948. | MR | Zbl

[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. | MR | Zbl

[19] V. Thomée: Difference methods for two dimensional mixed problems for hyperbolic first order systems. Arch. Rat. Mech. Anal., 8, 1961, p.68-88. | MR | Zbl

[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. | MR | Zbl

[21] B.L. Rozdestvenskii, N.N. Yanenko: Systems of quasilinear equations. Izd. Nauka Moskva, 1968.

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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'Université Fudan, 1960, p.17-28.

[26] Gu Chao-Hao: Une méthode pour résoudre le problème de l'écoulement supersonique autour d'une arête avec une frontière courbe. Bulletin de Fudan, 7, n°1, 1962, p.11-14.

[27] Gu Chao-Hao: A boundary value problem for hyperbolic systems and its applications. Acta Math. Sinica, 13, 1963, p.32-48. | MR | Zbl

[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. | MR | Zbl

[29] D.G. Schaeffer: Supersonic flow past a nearly straight wedge. Duke Math. J., 43, 1976, p.637-670. | MR | Zbl

[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. | MR | Zbl

[31] Li Ta-Tsien: On a free boundary problem. A paraître dans Chinese Annals of Math.

[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 de Fudan, 2, 1979, p.83-93.

[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'Université Fudan, 1960, p.1-16.

[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. | Zbl

[35] Gu Chao-Hao, Li Ta-Tsien, Ho Zon-Y: (II), ibid, 11, 1961, p.324-327.

[36] Gu Chao-Hao, Li Ta-Tsien, Ho Zon-Y: (III), ibid, 12, 1962, p.132-143.

[37] Li Ta-Tsien, Yu Wen-Tzu: Discontinuous solutions for the quasi-linear hyperbolic systems. A paraître.

[38] P.D. Lax: Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math., 10, 1957, p.537-566. | MR | Zbl

[39] J. Glimm: Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math., 18, 1965, p.697-715. | MR | Zbl