A note on the delay nonlinear parabolic differential equations

In this paper, the initial boundary value problem (IBVP) for nonlinear delay differential equations (DEs) in a Banach space with strongly unbounded operators is studied. The theorem on the existence and uniqueness of a bounded solution (BS) of this problem is established. The application of the main theorem to nonlinear delay parabolic equations is provided. Theorems on the existence and uniqueness of a bounded solution of the initial boundary value problems for three types of nonlinear delay parabolic equations are established. The first and second order of accuracy difference schemes (FSOADSs) for the solution of one dimensional nonlinear parabolic equation with time delay are presented. Finally, certain numerical experiments are given to confirm the agreement between experimental and theoretical results and to make clear how effective the proposed approach is.