4 papers · 1 filter
A PDE formulation of Lyapunov stability for contact-type Hamilton-Jacobi equations
Panrui Ni, Jun Yan
We study the Lyapunov stability of stationary solutions to contact-type Hamilton-Jacobi equations on a compact manifold. Previous works typically assume Tonelli Hamiltonians…
Static class-guided selection of elementary solutions in non-monotone vanishing discount problems
Panrui Ni, Jun Yan, Maxime Zavidovique
We study a generalized vanishing discount problem for Hamilton--Jacobi equations, removing the standard monotonicity assumption, either in a global sense or when integrated against…
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…
Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step
Panrui Ni
In this paper, we mainly focus on the existence of the viscosity solutions of \begin{equation*} \left\{ \begin{aligned} &H_1(x,Du_1(x),u_1(x),u_2(x))=0,\\ &H_2(x,Du_2(x),u_2(x),u_1…