A note on exponential-type solutions for the linear, delayed heat partial differential equation

TL;DR

This paper constructs exponential-type solutions for the linear delayed heat equation, aiding in solving boundary and initial-value problems in heat transfer, and analyzes their mathematical properties including delay dependence.

Contribution

It introduces a new class of exponential solutions for the delayed heat equation and explores their mathematical properties and potential applications.

Findings

Exponential solutions depend on the delay parameter.

Representations can serve as a priori ansatzes for boundary/initial problems.

Mathematical properties of solutions are systematically examined.

Abstract

We construct a class of exponential type solutions for the linear, delayed heat equation. These representations may be used to provide a priori ansatzes for certain boundary and/or initial-value problems arising in heat transfer. Several of the important mathematical properties of the representations are examined, including a discussion of the dependence on the delay parameter.