2017/07/20 by Daria Ghilli, Ghilli, Daria, Zhiping Rao +3
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1707.06592
openalex publication_date 2017/07/20 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
This paper deals with junction conditions for Hamilton-Jacobi-Bellman (HJB)\nequations for finite horizon control problems on multi-domains. We consider two\ndifferent cases where the final cost is continuous or lower semi-continuous. In\nthe continuous case we extend the results of "Hamilton-Jacobi-Bellman equations\non multi-domains" by the second and third authors in a more general framework\nwith switching running costs and weaker controllability assumptions. The\ncomparison principle has been established to guarantee the uniqueness and the\nstability results for the HJB system on such multi-domains. In the lower\nsemi-continuous case, we characterize the value function as the unique lower\nsemi-continuous viscosity solution of the HJB system, under a local\ncontrollability assumption.\n