What can we expect of the heat in a thin plate ?

TL;DR

This paper explores how linear algebra techniques can predict the behavior of heat distribution in thin rectangular plates through a simple domain perturbation example.

Contribution

It demonstrates the application of linear algebra to analyze PDEs in thin domains, providing a straightforward approach for understanding heat behavior.

Findings

Linear algebra effectively models heat distribution in thin plates.

Domain perturbation impacts heat behavior predictably.

Method offers a simplified analysis for PDEs in thin geometries.

Abstract

We illustrate, with a simple example of domain perturbation problem, how Linear Algebra can be applied to determine the behavior of a family of partial differential equations posed in a thin rectangular domain. (In portuguese)