Bounded Solutions of Semi-Linear Parabolic Differential Equations with Unbounded Delay Terms

In the present work, an initial boundary value problem (IBVP) for the semi-linear delay differential equation in a Banach space with unbounded positive operators is studied. The main theorem on the uniqueness and existence of a bounded solution (BS) of this problem is established. The application of the main theorem to four different semi-linear delay parabolic differential equations is presented. The first- and second-order accuracy difference schemes (FSADSs) for the solution of a one-dimensional semi-linear time-delay parabolic equation are considered. The new desired numerical results of this paper and their discussion are presented.

Automated summary

This work studies the initial boundary value problem (IBVP) for a semi-linear delay differential equation in a Banach space with unbounded positive operators. The main theorem establishes the uniqueness and existence of a bounded solution (BS) for this problem. Applications of the main theorem to four different semi-linear delay parabolic differential equations are presented. The paper also considers the first- and second-order accuracy difference schemes (FSADSs) for solving a one-dimensional semi-linear time-delay parabolic equation, presenting new numerical results and their discussion.