4 papers · 2 filters
Generalized Hamiltonian gradient flow of contact type II: singularities, cut locus, and controllability
Qingyang Cai, Wei Cheng, Tianqi Shi
We study singularities, cut loci and controllability for time-dependent contact Hamilton--Jacobi equations. A contact version of Arnaud's theorem identifies the superdifferential g…
On the cut locus of Hamilton--Jacobi equations I: structure and propagation via the touching approach
Piermarco Cannarsa, Wei Cheng, Jiahui Hong \and Wenxue Wei
For a semiconcave function with linear modulus, we introduce the cut locus through a touching approach and prove that it coincides with the variational cut locus defined via the La…
Generalized Hamiltonian gradient flow of contact type I: regularity of the fundamental solutions
Wei Cheng, Shengqing Hu, Kaizhi Wang
This paper studies generalized Hamiltonian gradient flows for contact-type Hamilton--Jacobi equations, adopting the variational framework of Herglotz's principle and its fundamenta…
Recent progress in generalized Hamiltonian gradient flow: Singularities
Wei Cheng, Jiahui Hong
This paper is a survey of the generalized Hamiltonian gradient flow (GHGF) framework for Hamilton-Jacobi equations, with an emphasis on the propagation of singularities and its con…