Hamilton-Jacobi Equations with State Constraints

Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints

We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary condition to asymptotic solutions as time goes to infinity.

On Hamilton–Jacobi–Bellman equations with convex gradient constraints

We study PDE of the form maxfF.D2u; x/ ! f .x/;H.Du/g D 0 where F is uniformly elliptic and convex in its first argument, H is convex, f is a given function and u is the unknown. These equations are derived from dynamic programming in a wide class of stochastic singular control problems. In particular, examples of these equations arise in mathematical finance models involving transaction costs,...

Hamilton-Jacobi-Bellman Equations

This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...

Viability Solutions to Structured Hamilton-Jacobi Equations under Constraints

Hamilton-Jacobi treatment of fields with constraints

In this paper the Gulers formalism for the systems with finite degrees of freedom is applied to the field theories with constraints. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi formulation. The Proca’s model is investigated in details.