Open Access Research

Well-posedness of delay parabolic difference equations

Allaberen Ashyralyev12* and Deniz Agirseven3

Author Affiliations

1 Department of Mathematics, Fatih University, Istanbul, 34500, Turkey

2 Department of Mathematics, ITTU, Gerogly Street, Ashgabat, 74400, Turkmenistan

3 Department of Mathematics, Trakya University, Edirne, 22030, Turkey

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Advances in Difference Equations 2014, 2014:18  doi:10.1186/1687-1847-2014-18

Published: 16 January 2014

Abstract

The well-posedness of difference schemes of the initial value problem for delay differential equations with unbounded operators acting on delay terms in an arbitrary Banach space is studied. Theorems on the well-posedness of these difference schemes in fractional spaces are proved. In practice, the coercive stability estimates in Hölder norms for the solutions of difference schemes of the mixed problems for delay parabolic equations are obtained.

Keywords:
well-posedness; delay parabolic equations; fractional spaces; coercive stability