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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…