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Abstrakty
We consider the Cauchy problem in an unbounded region for equations of the type either $D_{t}z(t,x) = f(t,x,z(t,x),z_{(t,x)},D_{x}z(t,x))$ or $D_{t}z(t,x)= f(t,x,z(t,x),z,D_{x}z(t,x))$. We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-16
Opis fizyczny
Daty
wydano
1996
otrzymano
1992-08-28
poprawiono
1996-02-09
Twórcy
autor
- Institute of Mathematics, University of Gdańsk, 57 Wita Stwosza St., 80-952 Gdańsk, Poland
Bibliografia
- [1] P. Besala, On solutions of first order partial differential equations defined in an unbounded zone, Bull. Acad. Polon. Sci. 12 (1964), 95-99.
- [2] P. Besala, Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations, Ann. Polon. Math. 46 (1985), 19-26.
- [3] Z. Kamont, On the Cauchy problem for system of first order partial differential equations, Serdica 5 (1979), 327-339.
- [4] M. Krzyżański, Partial Differential Equations of Second Order, PWN, Warszawa, 1971.
- [5] H. Leszczyński, General finite difference approximation to the Cauchy problem for non-linear parabolic differential-functional equations, Ann. Polon. Math. 53 (1991), 15-28.
- [6] H. Leszczyński, Uniqueness results for unbounded solutions of first order non-linear differential-functional equations, Acta Math. Hungar. 64 (1994), 75-92.
- [7] M. Malec et A. Schiaffino, Méthode aux différences finies pour une équation non-linéaire différentielle fonctionnelle du type parabolique avec une condition initiale de Cauchy, Boll. Un. Mat. Ital. (7) 1-B (1987), 99-109.
- [8] K. Prządka, Difference methods for non-linear partial differential functional equations of the first order, Math. Nachr. 138 (1988), 105-123.
- [9] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.
Typ dokumentu
Bibliografia
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