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math.AP2024
Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations
Andrea Davini, Panrui Ni, Jun Yan +1
We study the asymptotic behavior of solutions of an equation of the form \begin{equation}\label{abs}\tag{*} G\big(x, D_x u,λu(x)\big) = c_0\qquad\hbox{in } \end{equation} on a c…
math.AP2024
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…