Mixed problems for infinite systems of quasilinear hyperbolic functional differential equations

• Autorzy: Kozieł S.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with initial-boundary problems for quasilinear infinite systems of first order partial differential functional equations. The unknown function is the functional variable in the system, the partial derivatives appear in a classical sense. A theorem on the existence and uniqueness of the Caratheodory solution and continuous dependence upon initial-boundary data is proved. The mixed problem is equivalent in a suitable function space to a system of functional integral equations. Infinite differential systems with a deviated argument and differential integral problems can be derived from a general model by specializing given functions.

Słowa kluczowe

EN

differential equations; Cauchy problem; mixed problem

PL

równania różniczkowe; problem Cauchy'ego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 3
• Strony: 659--674
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kozieł S.

• Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland

Bibliografia

• [1] T. Człapiński, On the mixed problem for quasilinear partial differential-functional equations of the first order, Zeit. Anal. Anwend. 16 (1997), 463-478.
• [2] T. Człapiński, The mixed problem for an infinite system of first order functional differential equations, Univ. Iagell. Acta Math. 39 (2001), to appear.
• [3] T. Człapiński, Z. Kamont, On the local Cauchy problem for quasilinear hyperbolic functional differential systems, Appl. Anal. 64, 1997, 329-342.
• [4] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, Boston, London, 1999.
• [5] Z. Kamont, Infinite systems of hyperbolic functional differential inequalities, Nonl. Anal. TMA, to appear.
• [6] Z. Kamont, S. Kozieł, Infinite systems of differential difference inequalities and applications, J. Ineq. Appl., to appear.
• [7] J. Szarski, Cauchy problem for an infinite system of differential functional equations with first order partial derivatives, Ann. Soc. Math. Polon. Comm. Math., Spec. Vol. I, 1978, 293-300.
• [8] J. Szarski, Comparison theorems for infinite systems of differential-functional equations and strongly coupled infinite systems of first order partial differential equations, Rocky Mountain J. Math. 10 (1980), 237-246.
• [9] M. I. Umanaliev, J. A. Vied, On integral differential equations with first order partial derivatives, (Russian), Differen. Urav. 25 (1989), 465-477.