Metraipolis › archive › dc_44fffab108fd

Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space — arXiv:2611.01479

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01479
License (as archived): CC0-1.0
Archived: 2026-11-03T18:46:17.239Z
SHA-256 of the archived text: 07592c9917000cb0d032f7f50f9e209785d26c731e732c917467fd4f702ee15d
Stable URL of this page: https://metraipolis.com/documento/dc_44fffab108fd

How to cite

Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space — arXiv:2611.01479 — arXiv (en), https://arxiv.org/abs/2611.01479 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_44fffab108fd (Metraipolis archive dc_44fffab108fd, sha256 07592c9917000cb0d032f7f50f9e209785d26c731e732c917467fd4f702ee15d)

BibTeX

@misc{dc44fffab108fd,
  title = {Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space — arXiv:2611.01479},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01479},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_44fffab108fd; sha256 07592c9917000cb0d032f7f50f9e209785d26c731e732c917467fd4f702ee15d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01479. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We establish the long-time behavior of solutions $U$ to first-order Hamilton-Jacobi equations in the Wasserstein space $\mathcal{P}_2(\mathbb T^d)$. For a class of Hamiltonians with quadratic growth, including non-convex ones, we prove that there exist a unique ergodic constant $\lambda$ and a solution $V$ of the associated ergodic problem such that $U(t,m)-\lambda t$ converges to $V(m)$, uniformly on $\mathcal{P}_2(\mathbb T^d)$, as $t\to+\infty$. Finally, we provide applications to mean field control problems and zero-sum differential games.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Analysis of PDEs (math.AP) ; Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.01479 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:14:37.808Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).