# Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 2, page 177-191
- ISSN: 0066-2216

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topTomasz Człapiński. "Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations." Annales Polonici Mathematici 57.2 (1992): 177-191. <http://eudml.org/doc/262238>.

@article{TomaszCzłapiński1992,

abstract = {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.},

author = {Tomasz Człapiński},

journal = {Annales Polonici Mathematici},

keywords = {differential-functional system; second canonical form; generalized solutions; existence; uniqueness; continuous dependence upon boundary data},

language = {eng},

number = {2},

pages = {177-191},

title = {Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations},

url = {http://eudml.org/doc/262238},

volume = {57},

year = {1992},

}

TY - JOUR

AU - Tomasz Człapiński

TI - Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 2

SP - 177

EP - 191

AB - 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.

LA - eng

KW - differential-functional system; second canonical form; generalized solutions; existence; uniqueness; continuous dependence upon boundary data

UR - http://eudml.org/doc/262238

ER -

## References

top- [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. Zbl0355.35059
- [2] P. Bassanini, Iterative methods for quasilinear hyperbolic systems, ibid. (6) 1-B (1982), 225- 250. Zbl0488.35056
- [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.
- [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. Zbl0444.65034
- [5] L. Cesari, A boundary value problem for quasilinear hyperbolic systems, Riv. Mat. Univ. Parma 3 (1974), 107-131. Zbl0342.35036
- [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. Zbl0307.35063
- [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. Zbl0763.35055
- [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.
- [9] T. Człapiński and Z. Kamont, Generalized solutions of quasi-linear hyperbolic systems of partial differential-functional equations, to appear. Zbl0798.35149
- [10] J. Hale, Functional Differential Equations, Springer, New York 1971. Zbl0222.34003
- [11] Z. Kamont, Existence of solutions of first order partial differential-functional equations, Comment. Math. 25 (1985), 249-263. Zbl0609.35017
- [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. Zbl0614.35089
- [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. Zbl0637.35080
- [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. Zbl0658.35085
- [15] Z. Kamont and J. Turo, Generalized solutions of boundary value problems for quasilinear systems with retarded argument, Radovi Mat. 4 (1988), 239-260. Zbl0686.35074
- [16] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 2, Academic Press, New York 1969. Zbl0177.12403
- [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. Zbl0446.35064
- [18] A. Salvadori, Sul problema di Cauchy per una struttura ereditaria di tipo iperbolico. Esistenza, unicità e dipendenza continua, ibid. 32 (1983), 329-356.
- [19] J. Turo, A boundary value problem for quasilinear hyperbolic systems of hereditary partial differential equations, ibid. 34 (1985-86), 15-34.
- [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. Zbl0612.35082
- [21] J. Turo, Existence and uniqueness of solutions of quasilinear hyperbolic systems of partial differential-functional equations, Math. Slovaca 37 (1987), 375-387.
- [22] J. Turo, A boundary value problem for hyperbolic systems of differential-functional equations, Nonlinear Anal. 13 (1) (1989), 7-18. Zbl0678.35090

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