A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations
Abstract
In this paper, we consider the following Hamilton-Jacobi equation with initial condition: equation* cases ∂tu(x,t)+H(x,t,u(x,t),∂xu(x,t))=0, u(x,0)=φ(x). cases 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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