Lin Wang, Jun Yan
Published 2013-12-04, updated 2014-03-15Version 2
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)=\phi(x). \end{cases} \end{equation*} Under some assumptions on the convexity of $H(x,t,u,p)$ w.r.t. $p$, we develop a dynamical approach to viscosity solutions and show that there exists an intrinsic connection between viscosity solutions and certain minimal characteristics.
Comments: This paper has been withdrawn by the author due to a crucial error in Lemma 3.4
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