Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations
Tomasz Człapiński
Annales Polonici Mathematici, Tome 57 (1992), p. 177-191 / Harvested from The Polish Digital Mathematics Library

Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:262238
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     title = {Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations},
     journal = {Annales Polonici Mathematici},
     volume = {57},
     year = {1992},
     pages = {177-191},
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Tomasz Człapiński. Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations. Annales Polonici Mathematici, Tome 57 (1992) pp. 177-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p177bwm/

[000] [1] 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. | Zbl 0355.35059

[001] [2] P. Bassanini, Iterative methods for quasilinear hyperbolic systems, ibid. (6) 1-B (1982), 225- 250. | Zbl 0488.35056

[002] [3] P. Bassanini, The problem of Graffi-Cesari, in: Nonlinear Phenomena in Math. Sci., V. Lakshmikantham (ed.), Proc. Arlington 1980, Academic Press, 1982, 87-101.

[003] [4] P. Bassanini e E. Filliaggi, Schemi iterativi a accelerazione della convergenza per operatori di contrazione nel prodotto di due spazi di Banach, Atti Sem. Mat. Fis. Modena 28 (1979), 249-279. | Zbl 0444.65034

[004] [5] L. Cesari, A boundary value problem for quasilinear hyperbolic systems, Riv. Mat. Univ. Parma 3 (1974), 107-131. | Zbl 0342.35036

[005] [6] L. Cesari, A boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form, Ann. Scuola Norm. Sup. Pisa (4) 1 (1974), 311-358. | Zbl 0307.35063

[006] [7] T. Człapiński, On the Cauchy problem for quasilinear hyperbolic systems of partial differential-functional equations of the first order, Z. Anal. Anwendungen 10 (1991), 169-182. | Zbl 0763.35055

[007] [8] T. Człapiński, A boundary value problem for quasilinear hyperbolic systems of partial differen- tial-functional equations of the first order, Boll. Un. Mat. Ital. (7) 5-B (1991), 619-637.

[008] [9] T. Człapiński and Z. Kamont, Generalized solutions of quasi-linear hyperbolic systems of partial differential-functional equations, to appear. | Zbl 0798.35149

[009] [10] J. Hale, Functional Differential Equations, Springer, New York 1971. | Zbl 0222.34003

[010] [11] Z. Kamont, Existence of solutions of first order partial differential-functional equations, Comment. Math. 25 (1985), 249-263. | Zbl 0609.35017

[011] [12] Z. Kamont and 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. | Zbl 0614.35089

[012] [13] Z. Kamont and J. Turo, On the Cauchy problem for quasilinear hyperbolic systems with a retarded argument, Ann. Mat. Pura Appl. 143 (1986), 235-246. | Zbl 0637.35080

[013] [14] Z. Kamont and J. Turo, A boundary value problem for quasilinear hyperbolic systems with a retarded argument, Ann. Polon. Math. 47 (1987), 347-360. | Zbl 0658.35085

[014] [15] Z. Kamont and J. Turo, Generalized solutions of boundary value problems for quasilinear systems with retarded argument, Radovi Mat. 4 (1988), 239-260. | Zbl 0686.35074

[015] [16] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 2, Academic Press, New York 1969. | Zbl 0177.12403

[016] [17] N. Mattioli and M. C. Salvatori, A theorem of existence and uniqueness in nonlinear dispersive optics, Atti Sem. Mat. Fis. Univ. Modena 28 (1979), 405-424. | Zbl 0446.35064

[017] [18] A. Salvadori, Sul problema di Cauchy per una struttura ereditaria di tipo iperbolico. Esistenza, unicità e dipendenza continua, ibid. 32 (1983), 329-356.

[018] [19] J. Turo, A boundary value problem for quasilinear hyperbolic systems of hereditary partial differential equations, ibid. 34 (1985-86), 15-34.

[019] [20] J. Turo, On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order, Czechoslovak Math. J. 36 (111) (1986), 185-197. | Zbl 0612.35082

[020] [21] J. Turo, Existence and uniqueness of solutions of quasilinear hyperbolic systems of partial differential-functional equations, Math. Slovaca 37 (1987), 375-387.

[021] [22] J. Turo, A boundary value problem for hyperbolic systems of differential-functional equations, Nonlinear Anal. 13 (1) (1989), 7-18. | Zbl 0678.35090