6 citations · 18 across the 16 of their papers we have counts for
16 papers
On the inhomogeneous discounted Hamilton-Jacobi equations
Liang Jin, Jun Yan, Kai Zhao
In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} λ(x)u+h(x,d_x u)=c \quad \tag{} \end{equation} on a clos…
On the causal discontinuity of Morse spacetimes
Lucas Dahinden, Liang Jin
Morse spacetime is a model of singular Lorentzian manifold, built upon a Morse function which serves as a global time function outside its critical points. The Borde-Sorkin conject…
Variational construction of connecting orbits between Legendrian graphs
Liang Jin, Jun Yan, Kai Zhao
Motivated by the problem of global stability of thermodynamical equilibria in non-equilibrium thermodynamics formulated in a recent paper [12], we introduce some mechanisms for con…
Nonlinear semigroup approach to Hamilton-Jacobi equations -- A toy model
Liang Jin, Jun Yan, Kai Zhao
In this paper, we discuss the existence and multiplicity problem of viscosity solution to the Hamilton-Jacobi equation where is a closed ma…
Variational attraction of the KAM torus for the conformally symplectic system
Liang Jin, Jianlu Zhang, Kai Zhao
For the conformally symplectic system \[ \left\{ \begin{aligned} \dot{q}&=H_p(q,p),\quad(q,p)\in T^*\mathbb{T}^n\\ \dot p&=-H_q(q,p)-λp, \quad λ>0 \end{aligned} \right. \] with a p…
Global dynamics of contact Hamiltonian systems (I): monotone systems
Liang Jin, Jun Yan
This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (…
Smooth subsolutions of the discounted Hamilton-Jacobi equations
Xiyao Huang, Liang Jin, Jianlu Zhang +1
For the discounted Hamilton-Jacobi equation,we construct subsolutions which are indeed solutions on the projected Aubry set. The smoothnes…
Point-assigned distance-like functions on non-compact geodesic spaces
Xiaojun Cui, Liang Jin, Xifeng Su
On a complete, connected, locally compact, non-compact geodesic space , we assign each compact set a distance-like function. With the help of these functions, we obtain a ps…
Herglotz' variational principle and Lax-Oleinik evolution
Piermarco Cannarsa, Wei Cheng, Liang Jin +2
We develop an elementary method to give a Lipschitz estimate for the minimizers in the problem of Herglotz' variational principle proposed in \cite{CCWY2018} in the time-dependent…
The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling
Hitoshi Ishii, Liang Jin
We study the vanishing discount problem for a nonlinear monotone system of Hamilton-Jacobi equations. This continues the first author's investigation on the vanishing discount prob…
The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 1: linear coupling
Hitoshi Ishii
We establish a convergence theorem for the vanishing discount problem for a weakly coupled system of Hamilton-Jacobi equations. The crucial step is the introduction of Mather measu…
On class A Lorentzian 2-tori with poles II: Foliations by timelike lines
Liang Jin, Lu Peng, Xiaojun Cui
We show that if is a class A Lorentzian 2-torus with timelike poles, then there exists a Lipschitz foliation by complete future-directed timelike geodesics wit…
On class A Lorentzian 2-tori with poles I: Closed geodesics pass through poles
Lu Peng, Liang Jin, Xiaojun Cui
In this paper, by studying certain isometries on globally hyperbolic planes, we prove that if is a timelike pole on a class A Lorentzian 2-torus, then there exists a closed tim…
Exponential convergence of 1-graph of the solution semigroup of contact Hamilton-Jacobi equations
Liang Jin, Lin Wang
Under certain assumptions, we show that for the solution semigroup of evolutionary contact Hamilton-Jacobi equations, its 1-graph, as a pseudo Legendrian graph, converges exponenti…
A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect
Liang Jin, Lin Wang, Jun Yan
Based on a fixed point argument, we give a {\it dynamical representation} of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations…
Global viscosity solutions for eikonal equations on class A Lorentzian 2-tori
Liang Jin, Xiaojun Cui
On the Abelian cover of a class A Lorentzian 2-torus , we showed the existence of global viscosity solutions to the eikonal equation $$ g(\…