2013/05/24 by Guy Barles, Barles, Guy, Ariela Briani +3 · 2 citations
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Variational Analysis #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1305.5813
openalex publication_date 2013/05/24 · arxiv created 2014/01/24 · arxiv updated 2014/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space \RN. In this article we extend our results in several directions: (i) to more general domains; (ii) by considering finite horizon control problems; (iii) by weaken the controlability assumptions. We use a Bellman approach and our main results are to identify the right Hamilton-Jacobi-Bellman Equation (and in particular the right conditions to be put on the interfaces separating the regions where the dynamic and running cost are different) and to provide the maximal and minimal solutions, as well as conditions for uniqueness. We also provide stability results for such equations.