A Reconstruction Algorithm for a Semilinear Parabolic Inverse Problem

TL;DR

This paper introduces a reconstruction algorithm for identifying a semilinear term in a parabolic PDE using a single boundary measurement, leveraging spectral representation and Whitney extension techniques.

Contribution

The paper presents a novel reconstruction algorithm for semilinear terms in parabolic equations based on spectral and extension methods, advancing inverse problem solutions.

Findings

Successful reconstruction of semilinear terms from boundary data

Use of spectral representation enhances algorithm accuracy

Extension techniques enable handling of boundary conditions

Abstract

In this paper, we consider an inverse problem to determine a semilinear term of a parabolic equation from a single boundary measurement of Neumann type. For this problem, a reconstruction algorithm is established by the spectral representation for the fundamental solution of heat equation with homogeneous Neumann boundary condition and the Whitney extension theorem.