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arXiv · 2502.20871

Time-optimal problem in the space of probabilities measures

Yurii Averboukh·Ekaterina Kolpakova
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Abstract

This paper focuses on the value function in the time-optimal problem for a continuity equation in the space of probability measures. We derive the dynamic programming principle for this problem. In particular, we prove that the Kruzhkov transform of the value function is a unique discontinuous viscosity solution to the corresponding Dirichlet problem for the Hamilton-Jacobi equation. Finally, we establish the $\Gamma$-convergence of the value function in a perturbed problem to the value function in the unperturbed problem.

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Yurii Averboukh, Ekaterina Kolpakova. 2025-02-28. Time-optimal problem in the space of probabilities measures. https://arxiv.org/abs/2502.20871

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