5 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 dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits
Liang Jin, Jun Yan, Kai Zhao
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,…
Dynamics of globally minimizing orbits in contact Hamiltonian systems
Yang Xu, Jun Yan, Kai Zhao
In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the -limit set of globally mi…
Stability of solutions to contact Hamilton-Jacobi equation on the circle
Yang Xu, Jun Yan, Kai Zhao
Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity solutions for Hamilton-Jacobi equations, we study the Lyapunov stability and instability of…
Time periodic and almost periodic viscosity solutions of contact Hamilton-Jacobi equations on
Kaizhi Wang, Jun Yan, Kai Zhao
This paper concerns with the time periodic viscosity solution problem for a class of evolutionary contact Hamilton-Jacobi equations with time independent Hamiltonians on the torus…