Bilayer one-dimensional Convection–Diffusion–Reaction-Source problem: Analytical and numerical solution

Umbricht, Guillermo Federico; Rubio, Diana; Tarzia, Domingo Alberto

doi:10.1016/j.ijthermalsci.2024.109471

International Journal of Thermal Sciences

2025

DOI: 10.1016/j.ijthermalsci.2024.109471

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Bilayer one-dimensional Convection–Diffusion–Reaction-Source problem: Analytical and numerical solution

Guillermo Federico Umbricht,

Diana Rubio,

Domingo Alberto Tarzia

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Optimal Control of the Inverse Problem of the Burgers Equation for Representing the State of Sonic Vibration Velocity in Water

Qin,

Meng,

2024

Mathematics

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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.

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Optimal Control of the Inverse Problem of the Burgers Equation for Representing the State of Sonic Vibration Velocity in Water

Qin,

Meng,

2024

Mathematics

View full text Add to dashboard Cite

show abstract

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Bilayer one-dimensional Convection–Diffusion–Reaction-Source problem: Analytical and numerical solution

Cited by 1 publication

References 49 publications

Optimal Control of the Inverse Problem of the Burgers Equation for Representing the State of Sonic Vibration Velocity in Water

Optimal Control of the Inverse Problem of the Burgers Equation for Representing the State of Sonic Vibration Velocity in Water

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