2013/09/27 by P. Jameson Graber, Philip Jameson Graber, Graber, Philip Jameson
Computer Science · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic processes and financial applications #math.OC
paper · pdf · doi:10.48550/arxiv.1309.7189
openalex publication_date 2013/09/27 · arxiv created 2013/10/10 · arxiv updated 2013/10/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove existence of minimizers to this optimization problem as in a relaxed setting and characterize the minimizers as weak solutions to a mean field game type system of coupled partial differential equations. Furthermore, we prove existence and partial uniqueness of weak solutions to the PDE system. An interpretation in terms of mean field games is also discussed. Keywords: Hamilton-Jacobi equations, optimal control, nonlinear PDE, viscosity solutions, front propagation, mean field games