Submitted Paper

Inserted: 29 nov 2012
Last Updated: 29 nov 2012

Year: 2012

Abstract:

Characteristic curves of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. However this description is valid only for smooth solutions. For non-smooth "viscosity" solutions, which give rise to discontinuous velocity fields, this picture holds only up to the moment when trajectories hit a shock and cease to minimize the Lagrangian action. In this paper we show that for any convex Hamiltonian, a viscous regularization allows to construct a non-smooth flow that extends particle trajectories and determines dynamics inside the shock manifolds. This flow consists of integral curves of a particular velocity field, which is uniquely defined everywhere in the flow domain and is discontinuous on shock manifolds.

Download:

• dynamicsHJE_final.pdf