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Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space

  • Erhan Bayraktar
  • Antonios Zitridis
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Abstract

We establish the long-time behavior of solutions U to first-order Hamilton-Jacobi equations in the Wasserstein space ๐’ซ2(๐•‹d). For a class of Hamiltonians with quadratic growth, including non-convex ones, we prove that there exist a unique ergodic constant ฮป and a solution V of the associated ergodic problem such that $U(t,m)-ฮปt$ converges to V(m), uniformly on ๐’ซ2(๐•‹d), as tโ†’+โˆž. Finally, we provide applications to mean field control problems and zero-sum differential games.

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Cite

BibTeXRIS
BibTeX
@misc{bayraktar2026longtime,
  title = {{Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space}},
  author = {Erhan Bayraktar and Antonios Zitridis},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01479},
  eprint = {2611.01479},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01479},
}
RIS
TY  - UNPB
TI  - Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space
AU  - Erhan Bayraktar
AU  - Antonios Zitridis
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01479
UR  - https://arxiv.org/abs/2611.01479
AB  - We establish the long-time behavior of solutions U to first-order Hamilton-Jacobi equations in the Wasserstein space ๐’ซ_2(๐•‹^d). For a class of Hamiltonians with quadratic growth, including non-convex ones, we prove that there exist a unique ergodic constant ฮป and a solution V of the associated ergodic problem such that $U(t,m)-ฮปt$ converges to V(m), uniformly on ๐’ซ_2(๐•‹^d), as tโ†’+โˆž. Finally, we provide applications to mean field control problems and zero-sum differential games.
ER  -