Generic properties of generalized hyperbolic partial differential equations

• Autorzy: Dariusz Bielawski
• Języki publikacji: EN

Abstrakty

EN

The existence and uniqueness of solutions and convergence of successive approximations are considered as generic properties for generalized hyperbolic partial differential equations with unbounded right-hand sides.

Słowa kluczowe

EN

Darboux problem; generic property; existence and uniqueness of solutions; Bielecki's norms

Kategorie tematyczne

• 35L20: Initial-boundary value problems for second-order hyperbolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 2
• Strony: 107-115

Daty

wydano

1994

otrzymano

1993-03-03

poprawiono

1993-12-27

Twórcy

autor

Dariusz Bielawski

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Bibliografia

• [1] A. Alexiewicz and W. Orlicz, Some remarks on the existence and uniqueness of solutions of hyperbolic equations $z_xy = f(x,y,z,z_x,z_y)$, Studia Math. 15 (1956), 201-215.
• [2] A. Bielecki, Une remarque sur l'application de la méthode de Banach-Caccioppoli-Tikhonov dans la théorie de l'équation s = f(x,y,z,p,q), Bull. Acad. Polon. Sci. Cl. III 4 (1956), 265-268.
• [3] T. Costello, Generic properties of differential equations, SIAM J. Math. Anal. 4 (1973), 245-249.
• [4] G. Darbo, Punti uniti in transformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 84-92.
• [5] F. S. De Blasi and J. Myjak, Generic properties of hyperbolic partial differential equations, J. London Math. Soc. (2) 15 (1977), 113-118.
• [6] K. Goebel, Thickness of sets in metric spaces and its application in fixed point theory, habilitation thesis, Lublin, 1970 (in Polish).
• [7] P. Hartman and A. Wintner, On hyperbolic partial differential equations, Amer. J. Math., 74 (1952), 834-864.
• [8] A. Lasota and J. Yorke, The generic property of existence of solutions of differential equations in Banach space, J. Differential Equations 13 (1973), 1-12.