Well-posedness of delay parabolic difference equations
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
Advances in Difference Equations 2014, 2014:18 doi:10.1186/1687-1847-2014-18Published: 16 January 2014
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.