Trajectories of the ε-perturbed optimal control problem in R² converge subsequentially to the network Γ, and in the Eikonal case the value functions converge to the value function of the corresponding network optimal control problem.
On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities, volume 104 of Progress in Nonlinear Differential Equations and their Applications
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Approximation of an optimal control problem on a network with a perturbed problem in the whole space
Trajectories of the ε-perturbed optimal control problem in R² converge subsequentially to the network Γ, and in the Eikonal case the value functions converge to the value function of the corresponding network optimal control problem.