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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.