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arXiv · 2412.10747

Optimal control of a kinetic equation

Aaron Pim·Tristan Pryer·Alex Trenam
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Abstract

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal solutions exhibit a hypocoercive decay property, ensuring stability and robustness. Building on this framework, we develop a finite element discretisation that preserves the stability properties of the continuous system. The effectiveness and accuracy of the proposed method are validated through a series of numerical experiments, showcasing its ability to handle challenging PDE-constrained optimal control problems.

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Aaron Pim, Tristan Pryer, Alex Trenam. 2024-12-14. Optimal control of a kinetic equation. https://arxiv.org/abs/2412.10747

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