Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The paper deals with initial boundary value problems for nonlinear first order partial differential functional equations. A theorem on the uniqueness of generalized solutions is proved. It is based on a comparison result for functional differential inequalities in the Carathéodory sense. A theorem on generalized solutions of functional differential inequalities is presented.
Wydawca
Rocznik
Tom
Strony
25--36
Opis fizyczny
bibliogr. 13 poz.
Twórcy
autor
- Gdansk University of Technology, Department of Differential Equations ul. G. Narutowicza, 80-952 Gdańsk, Poland, czernous@mif.pg.gda.pl
Bibliografia
- [1] S. Cinquini, On hyperbolic systems of (nonlinear) partial differential equations in several independent variables, Ann. Mat. Pura Appl. 120(4) (1979), 201-214,in Italian.
- [2] M. Cinquini Cibrario, New research on systems of nonlinear partial differential equations in several independent variables, Rend. Sem. Mat. Fis. Univ. Milano, 52 (1982), 531-550 , in Italian.
- [3] M. Cinquini Cibrario, A class of systems of nonlinear partial differential equations in several independent variables, Ann. Mat. Pura Appl. 140(4) (1985), 223-253.
- [4] T. Człapinski, On the mixed problem for quasilinear partial differential - functional equations of the first order, Z. Anal. Anwendungen, 16(2) (1997), 463-478.
- [5] Z. Kamont, Hyperbolic functional differential inequalities and applications, Kluwer Academic Publishers, Dordrecht, 1999.
- [6] Z. Kamont and H. Leszczyński, Uniqueness result for the generalized entropy solutions to the Cauchy problem for first-order partial differential-functional equations, Z. Anal. Anwendungen 13(3) (1994), 477-491.
- [7] Z. Kamont and A. Salvadori, Uniqueness of solutions to hyperbolic functional-differential problems, Proceedings of the Second World Congress of Nonlinear Analysts, Part 7, Athens 1996, Nonlinear Anal. 30(7) (1997), 4585-4594 .
- [8] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations, Pitman (Advanced Publishing Program), Boston, MA, 1985.
- [9] V. Lakshmikantham and S. Leela, Differential and integral inequalities, Academic Press, New York and London, 1969.
- [10] J. Szarski, Differential inequalities, Państwowe Wydawnictwo Naukowe, Warszawa, 1965.
- [11] K. Topolski, On the uniqueness of viscosity solutions for first order partial differential functional equations, Ann. Polon. Math. 59(1) (1994), 65-75.
- [12] K. Topolski, Classical methods for viscosity solutions of differential-functional inequalities, Nonlinear World 4(1) (1997), 1-17.
- [13] T. D. Van, M. Tsuji and N. T. S. Duy, The Characteristic Method and Its Generalizations for First - Order Nonlinear Partial Differential Equations, Chapman and Hall/CRC, Boca Raton, London, 2000.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0004-0016