Asymptotic profile of solutions to the heat equation on thin plate with boundary heating

TL;DR

This paper analyzes the behavior of solutions to the heat equation on a thin plate with boundary heating, deriving an asymptotic profile as the plate's thickness approaches zero.

Contribution

It provides a new asymptotic analysis of the heat equation on thin plates with boundary heating as thickness tends to zero.

Findings

Derived the asymptotic profile of solutions as h → 0

Identified dominant terms in the solution behavior

Provided insights into boundary heat transfer effects

Abstract

In this section, we consider the heat equation on a plate with thickness h > 0 being heated by a heat source on upper and lower faces of the plate. We obtain an asymptotic profile of the solution as the thickness h > 0 approaches to zero.