Time-optimal problem in the space of probabilities measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915824935108608 |
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| author | Averboukh, Yurii Kolpakova, Ekaterina |
| author_facet | Averboukh, Yurii Kolpakova, Ekaterina |
| contents | 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 $Γ$-convergence of the value function in a perturbed problem to the value function in the unperturbed problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-optimal problem in the space of probabilities measures Averboukh, Yurii Kolpakova, Ekaterina Analysis of PDEs Optimization and Control Probability 49J20, 49J52, 49L25, 49N70, 91A23, 49K20, 82C22 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 $Γ$-convergence of the value function in a perturbed problem to the value function in the unperturbed problem. |
| title | Time-optimal problem in the space of probabilities measures |
| topic | Analysis of PDEs Optimization and Control Probability 49J20, 49J52, 49L25, 49N70, 91A23, 49K20, 82C22 |
| url | https://arxiv.org/abs/2502.20871 |