5 papers · 1 filter
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…
Long-time behavior of generalized gradient flows of solutions to Hamilton-Jacobi equations
Paolo Albano, Piermarco Cannarsa, Wei Cheng +1
We study the long-time behavior of the generalized gradient flow associated with solutions of the critical Hamilton-Jacobi equation for mechanical Hamiltonians on the flat torus. F…
Variational construction of singular characteristics and propagation of singularities
Piermarco Cannarsa, Wei Cheng, Jiahui Hong +1
On a smooth closed manifold , we introduce a novel theory of maximal slope curves for any pair with a semiconcave function and a Hamiltonian. By using the notion…