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1999 | 72 | 2 | 99-114
Tytuł artykułu

Nonlocal problems for first order functional partial differential equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Local existence of generalized solutions to nonlocal problems for nonlinear functional partial differential equations of first order is investigated. The proof is based on the bicharacteristics and successive approximations methods.
Rocznik
Tom
72
Numer
2
Strony
99-114
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-12-11
poprawiono
1999-04-15
Twórcy
autor
  • Department of Mathematics, Technical University of Gdańsk, Narutowicza 11/12, 80-952 Gdańsk, Poland
Bibliografia
  • [1] P. Bassanini, Su una recente dimostrazione cirza il problema di Cauchy per sistemi quasi lineari iperbolici, Boll. Un. Mat. Ital. B (5) 13 (1976), 322-335.
  • [2] P. Bassanini, On a recent proof concerning a boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form, ibid. A (5) 14 (1977), 325-332.
  • [3] P. Bassanini, Iterative methods for quasilinear hyperbolic systems, ibid. B (6) 1 (1982), 225-250.
  • [4] P. Bassanini e M. C. Salvatori, Un problema ai limiti per sistemi integrodifferenziali non lineari di tipo iperbolico, ibid. B (5) 18 (1981), 785-798.
  • [5] P. Brandi, Z. Kamont and A. Salvadori, Existence of weak solutions for partial differential-functional equations, preprint.
  • [6] L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation $u_x t = F(x,t,u,u_x)$, J. Appl. Math. Stochastic Anal. 3 (1990), 163-168.
  • [7] L. Byszewski, Theorem about existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation, Appl. Anal. 40 (1991), 173-180.
  • [8] L. Byszewski, Existence of a solution of a Fourier nonlocal quasilinear parabolic problem, J. Appl. Math. Stochastic Anal. 5 (1992), 43-68.
  • [9] L. Byszewski, Monotone iterative method for a system of nonlocal initial-boundary parabolic problems, J. Math. Anal. Appl. 177 (1993), 445-458.
  • [10] L. Byszewski and V. Lakshmikantham, Monotone iterative technique for nonlocal hyperbolic differential problem, J. Math. Phys. Sci. 26 (1992), 346-359.
  • [11] L. Cesari, A boundary value problem for quasilinear hyperbolic system, Riv. Mat. Univ. Parma 3 (1974), 107-131.
  • [12] L. Cesari, A boundary value problem for quasilinear hyperbolic system in the Schauder canonic form, Ann. Scuola Norm. Sup. Pisa (4) 1 (1974), 311-358.
  • [13] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131.
  • [14] M. Cinquini-Cibrario e S. Cinquini, Equazioni alle derivate parziali di tipo iperbolico, Cremonese, Roma, 1964.
  • [15] T. Człapiński, On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations, preprint.
  • [16] 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.
  • [17] T. Człapiński and Z. Kamont, Generalized solutions of quasi-linear hyperbolic systems of partial differential-functional equations, J. Math. Anal. Appl. 172 (1993), 353-370.
  • [18] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kl-wer, 1999, to appear.
  • [19] 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. B (6) 4 (1985), 901-916.
  • [20] Z. Kamont and J. Turo, A boundary value problem for quasilinear hyperbolic systems with a retarded argument, Ann. Polon. Math. 47 (1987), 347-360.
  • [21] A. Pliś, Generalization of the Cauchy problem for a system of partial differential equations, Bull. Acad. Polon. Sci. Cl. III 4 (1956), 741-744.
  • [22] P. Pucci, Problemi ai limiti per sistemi di equazioni iperboliche, Boll. Un. Mat. Ital. B (5) 16 (1979), 87-99.
  • [23] J. Szarski, Generalized Cauchy problem for differential-functional equations with first order partial derivatives, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 575-580.
  • [24] J. Turo, On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order, Czechoslovak Math. J. 36 (1986), 185-197.
  • [25] J. Turo, Generalized solutions of the Cauchy problem for nonlinear functional partial differential equations, Z. Anal. Anwendungen 7 (1988), 127-133.
  • [26] J. Turo, Generalized solutions to functional partial differential equations of the first order, Zeszyty Nauk. Politech. Gdańskiej Mat. 14 (1988), 1-99.
  • [27] J. Turo, A boundary value problem for hyperbolic systems of differential-functional equations, Nonlinear Anal. 13 (1989), 7-18.
  • [28] J. Turo, Classical solutions to nonlinear hyperbolic functional partial differential equations, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.), to appear.
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Bibliografia
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