Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations
We study the asymptotic behavior of solutions of an equation of the form\begin
{equation}\label {abs}\tag {*} G\big (x, D_x u,\lambda u (x)\big)= c_0\qquad\hbox {in $ M …
{equation}\label {abs}\tag {*} G\big (x, D_x u,\lambda u (x)\big)= c_0\qquad\hbox {in $ M …
Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem
P Ni - Proceedings of the American Mathematical Society, 2023 - ams.org
Consider the generalized discounted Hamilton-Jacobi equation\[\lambda a (x) u+ H (x, Du)=
c (H),\] where $ a (x) $ may vanish or change the signs. Two examples are given in this …
c (H),\] where $ a (x) $ may vanish or change the signs. Two examples are given in this …
On the dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits
L Jin, J Yan, K Zhao - arXiv preprint arXiv:2501.01279, 2025 - arxiv.org
This paper is a continuation of our study of the dynamics of contact Hamiltonian systems
in\cite {JY}, but without monotonicity assumption. Due to the complexity of general cases, we …
in\cite {JY}, but without monotonicity assumption. Due to the complexity of general cases, we …
Variational construction of connecting orbits between Legendrian graphs
L Jin, J Yan, K Zhao - arXiv preprint arXiv:2208.13199, 2022 - arxiv.org
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 …
thermodynamics formulated in a recent paper [12], we introduce some mechanisms for …