Green's Functions of Partial Differential Equations with Involutions

TL;DR

This paper introduces a method to derive Green's functions for PDEs with involutions by transforming them into higher-order PDEs without involutions, demonstrated on a heat transfer model in a bent conducting plate.

Contribution

It presents a novel approach to handle PDEs with involutions by reduction to higher-order PDEs, expanding analytical tools for such equations.

Findings

Successfully derived Green's functions for PDEs with involutions.

Applied the method to a heat transfer problem in a bent plate.

Demonstrated the effectiveness of the approach in a practical model.

Abstract

In this paper we develop a way of obtaining Green's functions for partial differential equations with linear involutions by reducing the equation to a higher-order PDE without involutions. The developed theory is applied to a model of heat transfer in a conducting plate which is bent in half.