The method of characteristics revisited. A viability approach

1999/06/25 by Jean-Pierre Aubin, Aubin, Jean-Pierre
Mathematics · #34C35 #34K35 #49L05 #49L25 #70H20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:34C35 #msc:34K35 #msc:49L05 #msc:49L25 #msc:70H20

paper · pdf · doi:10.48550/arxiv.math/9906178

arxiv created 1999/06/25 · arxiv updated 2009/11/30

Abstract

This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these results are indeed useful for the treatment of hybrid systems of control theory. We rely on tools forged by set-valued analysis and viability theory, which happen to be both efficient and versatile to cover many problems. They find here unexpected relevance.

Related

• Mean viability theorems and second-order Hamilton-Jacobi equations
• Characteristic curves for set-valued Hamilton-Jacobi equations
• A Hamilton-Jacobi approach of sensitivity of ODE flows and switching points in optimal control problems
• An Update to the Level Set Theorems in Hamilton-Jacobi Reachability Analysis
• Exploiting characteristics in stationary action problems