Czasopismo
2004
|
Vol. 44, nr 2
|
217-226
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
We consider the initial value problem for second order differential - functional parabolic equation. Functional dependence is of the Hale type. On the basis of differential inequalities and fixed point method we prove the existence theorem for classical solution. Our formulation covers a large group of nonlocal problems such as , integro-differential equations, and "retarded and deviated" argument. We put particular stress on the last one, as it requires more general treatment.
Słowa kluczowe
Rocznik
Tom
Strony
217-226
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Institute of Mathematics, University of Gdańsk, Wit Stwosz 57, 80-952 Gdańsk, Poland, matkt@math.univ.gda.pl
Bibliografia
- [1] A. Belleni-Morante, An integro-differential equation arising from the theory of heat conduction in rigid materials with memory, Boll, Un. Mat. Ital.5, 15-B, (1978), 470-482.
- [2] S. Brzychczy, Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain. Ann. Polon. Math. 47 (1987), 309-317.
- [3] L. Byszewski. Monotone iterative method fpr a system of nonlocal initial-boundary parabolic problems, J. Math. Anal. Appl. 177 (2) (1993), 445-458.
- [4] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
- [5] J. Hale, Theory of Functional Differential Equations, Springer-Verlag New York Heidelberg Berlin 1977.
- [6] J. Hate and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag New York 1993.
- [7] O. A. Ladyzhenskaya, V. A. Solonikov and N. N. Uralceva, Linear and Quasilinear Equation of Parabolic Type, Nauka, Moskva, 1967 [Russian], (Translation of Mathematical Monographs, Vol.23, Am.Math.Soc., Providence, R.I., 1968.).
- [8] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations; Pitman Advanced Publishing Program, Boston - London - Melbourne, 1985.
- [9] H. Leszczyński, A new existence result for a non-linear heat equation with functional dependence, Comment. Math. 37 (1997) 155-181.
- [10] H. Leszczyński, On a nonlinear heat equation with functional dependence, to appear in Appl. Anal.
- [11] C. V. Pao, Coupled nonlinear parabolic systems with time delays, J. Math. Anal. Appl. 196 (1995), 237-265.
- [12] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.
- [13] K. A.Topolski, Parabolic differential-functional inequalities in a viscosity sense, Ann. Polon. Math. 68 (1998), 17-25.
- [14] K. A. Topolski, On the existence of classical solutions for differential - functional IBVP, Abstr. Appl. Anal. 3 (1998), no. 3-4, 363-375.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0002-0105