Generalized comparison principle for contact Hamilton-Jacobi equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912650817961984 |
|---|---|
| author | Liu, Gengyu Zhang, Jianlu |
| author_facet | Liu, Gengyu Zhang, Jianlu |
| contents | In this paper, we discuss all the possible pairs $(u,c)\in C(M,\mathbb R)\times\mathbb R$ solving (in the sense of viscosity) the contact Hamilton-Jacobi equation \[ H (x, d_xu, u) = c,\quad x\in M \] of which $M$ is a closed manifold and the continuous Hamiltonian $H: (x,p,u)\in T^*M\times\mathbb R\rightarrow\mathbb R$ is convex, coercive in $p$ but merely non-decreasing in $u$. Firstly, we propose a comparison principle for solutions by using the dynamical information of Mather measures. We then describe the structure of $\mathfrak C$ containing all the $c\in\mathbb R$ makes previous equation solvable. We also propose examples to verify the optimality of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized comparison principle for contact Hamilton-Jacobi equations Liu, Gengyu Zhang, Jianlu Dynamical Systems Analysis of PDEs 35B40, 35B51, 35F21, 37J50, 37J55, 49L25 In this paper, we discuss all the possible pairs $(u,c)\in C(M,\mathbb R)\times\mathbb R$ solving (in the sense of viscosity) the contact Hamilton-Jacobi equation \[ H (x, d_xu, u) = c,\quad x\in M \] of which $M$ is a closed manifold and the continuous Hamiltonian $H: (x,p,u)\in T^*M\times\mathbb R\rightarrow\mathbb R$ is convex, coercive in $p$ but merely non-decreasing in $u$. Firstly, we propose a comparison principle for solutions by using the dynamical information of Mather measures. We then describe the structure of $\mathfrak C$ containing all the $c\in\mathbb R$ makes previous equation solvable. We also propose examples to verify the optimality of our approach. |
| title | Generalized comparison principle for contact Hamilton-Jacobi equations |
| topic | Dynamical Systems Analysis of PDEs 35B40, 35B51, 35F21, 37J50, 37J55, 49L25 |
| url | https://arxiv.org/abs/2509.17310 |