11 papers
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…
Global propagation of singularities for magnetic mechanical systems
Piermarco Cannarsa, Wei Cheng, Jiahui Hong +1
We prove that singularities propagate globally for viscosity solutions of Hamilton-Jacobi equations related to magnetic mechanical systems on closed Riemannian manifolds. Our main…
Qualitative Estimates of Topological Entropy for Non-Monotone Contact Lax-Oleinik Semiflow
Wei Cheng, Jiahui Hong, Zhi-Xiang Zhu
For the non-monotone Hamilton-Jacobi equations of contact type, the associated Lax-Oleinik semiflow is expansive. In this paper, we provide qualitative estimates for…
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…
Optimal transport in the frame of abstract Lax-Oleinik operator revisited
Wei Cheng, Jiahui Hong, Tianqi Shi
This is our first paper on the extension of our recent work on the Lax-Oleinik commutators and its applications to the intrinsic approach of propagation of singularities of the vis…
Topological and control theoretic properties of Hamilton-Jacobi equations via Lax-Oleinik commutators
Piermarco Cannarsa, Wei Cheng, Jiahui Hong
In the context of weak KAM theory, we discuss the commutators and of Lax-Oleinik operators. We characteriz…
Topology of singular set of semiconcave function via Arnaud's theorem
Tianqi Shi, Wei Cheng, Jiahui Hong
We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The pr…
Local strict singular characteristics II: existence for stationary equation on
Wei Cheng, Jiahui Hong
The notion of strict singular characteristics is important in the wellposedness issue of singular dynamics on the cut locus of the viscosity solutions. We provide an intuitive and…
Global propagation of singularities for discounted Hamilton-Jacobi equations
Cui Chen, Jiahui Hong, Kai Zhao
The main purpose of this paper is to study the global propagation of singularities of viscosity solution to discounted Hamilton-Jacobi equation \begin{equation}\label{eq:discount 1…
Local strict singular characteristics: Cauchy problem with smooth initial data
Wei Cheng, Jiahui Hong
Main purpose of this paper is to study the local propagation of singularities of viscosity solution to contact type evolutionary Hamilton-Jacobi equation $$ D_tu(t,x)+H(t,x,D_xu(t,…
Representation formulas for contact type Hamilton-Jacobi equations
Jiahui Hong, Wei Cheng, Shengqing Hu +1
We discuss various kinds of representation formulas for the viscosity solutions of the contact type Hamilton-Jacobi equations by using the Herglotz' variational principle.