Sinc Approximation of the Heat Distribution on the Boundary of a Two-Dimensional Finite Slab

TL;DR

This paper develops a Sinc series-based method to approximate the heat distribution on the boundary of a 2D finite slab, addressing an ill-posed inverse problem with error estimates.

Contribution

It introduces a Sinc approximation approach for a 2D heat distribution inverse problem and provides error estimates for the method.

Findings

The Sinc series approximation effectively reconstructs the heat distribution.

Error bounds are established for the approximation.

The method addresses the ill-posedness of the inverse problem.

Abstract

We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation function is represented by a two-dimensional Sinc series and the error estimate is given.