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math.DS2013★ 1 cited
Weak KAM theorem for Hamilton-Jacobi equations
Xifeng Su, Jun Yan
In this paper, we generalize weak KAM theorem from positive Lagrangian systems to "proper" Hamilton-Jacobi equations. We introduce an implicitly defined solution semigroup of evolu…
math.DS2013
A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations
Lin Wang, Jun Yan
In this paper, we consider the following Hamilton-Jacobi equation with initial condition: \begin{equation*} \begin{cases} \partial_tu(x,t)+H(x,t,u(x,t),\partial_xu(x,t))=0, u(x,0)=…