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The method of quasilinearization for system of hyperbolic functional differential equations

Karpowicz A.

Commentationes Mathematicae

2008

Vol. 48, [Z] 2

155-168

We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations. [zob. pełny tekst: http://www.staff.amu.edu.pl/~commath/papers/482/4825.pdf]

A system for implicit impulsive nonlinear parabolic functional-differential inequalities

Byszewski L.

Fasciculi Mathematici

2007

Nr 37

5-18

A theorem about a system of weak implicit impulsive nonlinear parabolic functional-differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, maximum principles for the system of implicit impulsive nonlinear parabolic functional-differential inequalities and the uniqueness of a classical solution of a mixed implicit impulsive problem for a system of nonlinear parabolic functional-differential equations are obtained.

Differential difference inequalities generated by infinite systems of parabolic functional differential equations

Kozieł S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 1

99--126

The paper deals with the initial boundary value problem for infinite systems of parabolic functional differential equations. A comparison theorem concerning infinite systems of differential difference inequalities generated by the original problem is proved. The comparison result is used in an existence theorem and in investigating the stability of the numerical method of lines. A theorem on the error estimate of the metod is given.