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 $M$ is a compact manifold…