Inverse source problem for the parabolic equation with sparse moving observations

TL;DR

This paper addresses the inverse problem of locating a source in parabolic equations using sparse, moving boundary measurements, establishing uniqueness, proposing a reconstruction algorithm, and validating it through numerical experiments.

Contribution

It introduces a new approach for source identification with moving sensors, proving uniqueness and developing an effective reconstruction algorithm.

Findings

Proved the uniqueness of the inverse problem with sparse moving observations.

Developed a reconstruction algorithm based on sensor movement strategy.

Numerical experiments demonstrate the algorithm's effectiveness.

Abstract

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of the inverse problem under such measurements. Then the movement strategy of the sensor is given, from which the authors build the reconstruction algorithm. Finally, some numerical experiments are performed and the corresponding results are generated, which indicate the effectiveness of the algorithms.