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math.AP2026
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…
math.AP2026
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…
math.AP2025
Lyapunov stability and uniqueness problems for Hamilton-Jacobi equations without monotonicity
Yuqi Ruan, Kaizhi Wang, Jun Yan
We consider the evolutionary Hamilton-Jacobi equation \begin{align*} w_t(x,t)+H(x,Dw(x,t),w(x,t))=0, \quad(x,t)\in M\times [0,+\infty), \end{align*} where is a compact manifold…