Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914401858093056 |
|---|---|
| author | Gomoyunov, Mikhail |
| author_facet | Gomoyunov, Mikhail |
| contents | We study minimax (generalized) solutions of a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with co-invariant derivatives under a right-end boundary condition. Under assumptions on the Hamiltonian that are more general than those previously considered in the literature and allow, in particular, a measurable dependence on the first (time) variable, we establish existence, uniqueness, stability, and consistency results for minimax solutions. As an application, we consider a zero-sum differential game for a time-delay system and prove that this game has a value under assumptions more general than the known ones but rather natural being consistent with the Carathéodory conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games Gomoyunov, Mikhail Optimization and Control Analysis of PDEs 35F25, 49L12, 49L25, 49N70 We study minimax (generalized) solutions of a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with co-invariant derivatives under a right-end boundary condition. Under assumptions on the Hamiltonian that are more general than those previously considered in the literature and allow, in particular, a measurable dependence on the first (time) variable, we establish existence, uniqueness, stability, and consistency results for minimax solutions. As an application, we consider a zero-sum differential game for a time-delay system and prove that this game has a value under assumptions more general than the known ones but rather natural being consistent with the Carathéodory conditions. |
| title | Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games |
| topic | Optimization and Control Analysis of PDEs 35F25, 49L12, 49L25, 49N70 |
| url | https://arxiv.org/abs/2603.16168 |