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A problem for the hyperbolic system of differential equation without initial conditions

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Abstrakty
EN
In the present paper we consider a problem for the system of hyperbolic equations of the first order with periodic conditions and without initial conditions. Some conditions for uniqueness and existence of solution for this problem are given.
Wydawca
Rocznik
Strony
387--400
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • University of Rzeszów, Institute of Mathematics, Rejtana 16A, 35-959 Rzeszów, Poland
Bibliografia
  • [1] J. P. Aubin, Approximation of Elliptic Boundary - Value Problems, Wiley-Interscience, New York-London-Sydney-Toronto, 1972.
  • [2] D. Bainov, E. Minchev, E. Myszkis, Periodic boundary value problems for impulsive hyperbolic systems, Comm. Appl. Anal. 1, No 1 (1997), 1-14.
  • [3] R. Courant, Partial Differential Equations, New York-London 1962.
  • [4] V. M. Kyrylich, A. D. Myszkis, Boundary value problem without initial conditions for linear hyperbolic system with two independent variables, Dopov. Dokl. Akad. Nauk Ukraini Math. Prirodozn. Tekh. No 5 (1991), 8-10 (in Ukrainien).
  • [5] V. M. Kyrylich, A. D. Myszkis, Boundary value problems without initial conditions for linear homogenous hyperbolic system, Differ. Uravn. T. 28, No 3 (1992), 463-465 (in Russian).
  • [6] S. P. Lavrenyuk, L. Zaręba, Nonlocal problem for the nonlinear hyperbolic system of the first order without initial condition, Math. Stud. T. 14, No 2 (2000), 150-158.
  • [7] J. L. Lions, Quelques méthodes de résolution des problémes aux limites non lineaires, Paris 1969.
  • [8] Z. O. Mel'nyk, V. M. Kyrylich, Nonlocal problems without initial conditions for hyperbolic equations and systems with two independent variables, Ukrain. Mat. Zh. No 6 (1983), 722-727.
  • [9] Z. O. Mel'nyk, One nonclasical boundary problem for hyperbolic system of the first order with two independents variables, Differ. Uravn. 17, No 6 (1981), 1096-1104.
  • [10] J. Muszyński, J. Radzikowski, Boundedness of solution of some hyperbolic system, Demonstratio Math. Vol. 4 (1976), 747-761.
  • [11] A. D. Myszkis, W. E. Abolina, The mixed problem for semilinear hyperbolic system on the area, Matem. Sborn. No 4 (1960), 423-442 (in Russian).
  • [12] M. M. Potapow, The global solution of the mixed problem for semilinear hyperbolic system of the first order, Differ. Uravn. No 10 (1983), 1826-1828 (in Russian).
  • [13] J. Radzikowski, On the existence of a solution of the mixed problem for a certain hyperbolic system, Demonstratio Math. Vol. 21, No 1 (1988), 59-75.
  • [14] J. Radzikowski, The existence of a solution of the mixed problem for a certain symmetric t-hyperbolic system, Demonstratio Math. Vol. 17, No 4 (1984), 913-938.
  • [15] P. Smoczyński, Semilinear mixed problem for hyperbolic system of equations in two independet variables within the class of measurable solution, Bull. Polish Acad. Sci. Math. 31, No 3, 4 (1983), 129-136.
  • [16] M. Taniguchi, Mixed problem for hyperbolic systems of the first order, Publ. Res. Inst. Math. Sci., Kyoto Univ. No 8 (1971), 471-481.
  • [17] W. Zajączkowski, A priori estimates for solutions to noncharacteristic mixed problems to nonlinear symmetric hyperbolic system of the first order with dissipation, Bull. Polish Acad. Sci. Math. 37, No 1-6 (1989), 183-197.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0013-0012
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