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arXiv · 1312.1072

A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations

Lin Wang·Jun Yan
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Abstract

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)=ϕ(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.

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Lin Wang, Jun Yan. 2014-03-15. A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations. https://arxiv.org/abs/1312.1072

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