Inverse source problem for the parabolic equation with sparse moving observations
Provides theoretical and algorithmic advances for inverse source problems with moving sensors, relevant to applied mathematics and engineering.
The paper proves uniqueness for identifying source terms in parabolic equations using sparse moving boundary measurements and proposes a reconstruction algorithm, with numerical experiments demonstrating effectiveness.
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.