On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables
Czechoslovak Mathematical Journal, Tome 41 (1991) no. 3, pp. 490-506
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

DOI : 10.21136/CMJ.1991.102483
Classification : 35D05, 35F20, 35R10
@article{10_21136_CMJ_1991_102483,
     author = {Cz{\l}api\'nski, Tomasz},
     title = {On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables},
     journal = {Czechoslovak Mathematical Journal},
     pages = {490--506},
     year = {1991},
     volume = {41},
     number = {3},
     doi = {10.21136/CMJ.1991.102483},
     mrnumber = {1117802},
     zbl = {0797.35159},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1991.102483/}
}
TY  - JOUR
AU  - Człapiński, Tomasz
TI  - On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables
JO  - Czechoslovak Mathematical Journal
PY  - 1991
SP  - 490
EP  - 506
VL  - 41
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1991.102483/
DO  - 10.21136/CMJ.1991.102483
LA  - en
ID  - 10_21136_CMJ_1991_102483
ER  - 
%0 Journal Article
%A Człapiński, Tomasz
%T On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables
%J Czechoslovak Mathematical Journal
%D 1991
%P 490-506
%V 41
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1991.102483/
%R 10.21136/CMJ.1991.102483
%G en
%F 10_21136_CMJ_1991_102483
Człapiński, Tomasz. On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables. Czechoslovak Mathematical Journal, Tome 41 (1991) no. 3, pp. 490-506. doi: 10.21136/CMJ.1991.102483

[1] P. Bassanini: Su una recente dimostrazione cirza il problema di Cauchy per sistemi quasi lineari iperbolici. Boll. Un. Mat. Ital. (5) 13-B (1976), 322-335. | MR

[2] P. Bassanini: On a recent proof concerning a boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form. Boll. Un. Mat. Ital. (5) 14-A (1977), 325-332. | MR | Zbl

[3] P. Bassanini: Iterative methods for quasilinear hyperbolic systems. Boll. Un. Mat. Ital. (6) 1-B (1982), 225-250. | MR | Zbl

[4] P. Bassanini M. C. Salvatori: Un problema ai limiti per sistemi integrodifferenziali non lineari di tipo iperbolico. Boll. Un. Mat. Ital. (5) 18-B (1981), 785-798. | MR

[5] P. Brandi R. Ceppitelli: On the existence of the solution of a nonlinear functional partial differential equations of the first order. Atti. Sem. Mat. Fis. Univ. Modena 29 (1980), 166-186. | MR

[6] P. Brandi R. Ceppitelli: Existence, uniqueness and continuous dependence for a first order non linear partial differential equation in a hereditary structure. Ann. Polon. Math. 47 (1986), 121-136. | DOI | MR

[7] L. Cesari: A boundary value problem for quasilinear hyperbolic systems. Riv. Mat. Univ. Parma 3 (1974), 107-131. | MR

[8] L. Cesari: A boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form. Ann. Sc. Norm. Sup. Pisa (4) 1 (1974), 311 - 358. | MR

[9] M. Cinquini-Cibrario S. Cinquini: Equazioni alle derivate parziali di tipo iperbolico. Cremonese, Roma 1964. | MR

[10] Z. Kamont: On the Cauchy problem for nonlinear partial differential-functional equations of the first order. Math. Nachr. 88 (1979), 13-29. | DOI | MR

[11] Z. Kamont: On the estimation of the existence domain for solutions of a nonlinear partial differential-functional equation of the first order. Glasnik Mat. 13 (1978), 277-291. | MR

[12] Z. Kamont: Existence of solutions of first order partial differential-functional equations. Ann. Soc. Math. Polon., Ser. I: Comm. Math. 25 (1985), 249-263. | MR | Zbl

[13] Z. Kamont J. Turo: On the Cauchy problem for quasilinear hyperbolic system of partial differential equations with a retarded argument. Boll. Un. Mat. Ital. (6) 4-B (1985), 901 - 916. | MR

[14] Z. Kamont J. Turo: A boundary value problem for quasilinear hyperbolic systems with a retarded argument. Ann. Polon. Math. 47 (1987), 347-360. | DOI | MR

[15] Z. Kamont S. Zacharek: On the existence of weak solutions of nonlinear first order partial differential equations in two independent variables. Boll. Un. Mat. Ital. (6) 5-B (1986), 851-879. | MR

[16] S. N. Kruzhkov: Generalized solutions of non linear first order partial differential equations. (Russian), Mat. Sb. 70 (1966), 394-415.

[17] O. A. Oleynik: Discontinuous solutions of non linear differential equations. (Russian), Usp. Mat. Nauk. 12, 3 (1957), 3-73. | MR

[18] P. Pucci: Problemi ai limiti per sistemi di equazioni iperboliche. Boll. Un. Mat.Ital. (5) 16-B (1979), 87-99. | Zbl

[19] B. L. Rozhdestvenskij N. N. Yanenko: Systems of quasilinear equations and their applications to gas dynamics. Providence, Rhode Island 1983.

[20] J. Turo: A boundary value problem for quasilinear hyperbolic systems of hereditary partial differential equations. Atti. Sem. Mat. Fis. Univ. Modena 34 (1985-86), 15-34. | MR

[21] J. Turo: On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order. Czech. Math. J. 36 (111) (1986), 185-197. | MR | Zbl

[22] J. Turo: Generalized solutions to functional partial differential equations of the first order. Zesz. Nauk. Polit. Gd. 427, Mat. 14 (1988), 3-98. | Zbl

Cité par Sources :