Well-posedness of delay parabolic equations with unbounded operators acting on delay terms
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
Boundary Value Problems 2014, 2014:126 doi:10.1186/1687-2770-2014-126Published: 20 May 2014
In the present paper, the well-posedness of the initial value problem for the delay differential equation , ; () in an arbitrary Banach space E with the unbounded linear operators A and in E with dense domains is studied. Two main theorems on well-posedness of this problem in fractional spaces are established. In practice, the coercive stability estimates in Hölder norms for the solutions of the mixed problems for delay parabolic equations are obtained.