Weak KAM theory for general Hamilton-Jacobi equations I: the solution semigroup under proper conditions

Xifeng Su, Lin Wang, Jun Yan

We consider the following evolutionary Hamilton-Jacobi equation with initial condition: \begin{equation*} \begin{cases} \partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=ϕ(…