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math.AP2014★ 1 cited
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(…
math.AP2014★ 1 cited
Weak KAM theory for general Hamilton-Jacobi equations II: the fundamental solution under Lipschitz conditions
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(…
math.AP2014
Weak KAM theory for general Hamilton-Jacobi equations III: the variational principle under Osgood conditions
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(…