Optimal Control of the Inverse Problem of the Burgers Equation for Representing the State of Sonic Vibration Velocity in Water
Year: 2024
Type: article
Abstract: In this paper, we investigate the inverse of the set of unknown functions (v,g) of the Burgers equation in the framework of optimal theory. Firstly, we prove the existence of functional minimizers in the optimal control problem and derive the necessary conditions for the optimal solution. Subsequently, the global uniqueness of the optimal solution and its stability are explored. After completing the ill-posed analysis of the Burgers equation, we can apply it to the problem of sonic vibration velocity in water. The desired result is obtained by inverse-performing an unknown initial state with known terminal vibration velocity. This is important for solving practical problems.
Source: Mathematics
DOI: 10.3390/math12223625
Authors: Jiale Qin, Yiping Meng, Shichao Yi
Institution: Jiangsu University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4404567934