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Hamilton-Jacobi equations constrained on networks. (English) Zbl 1268.35120

Summary: We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a network. In our setting, the value function is continuous. We define a notion of constrained viscosity solution of Hamilton-Jacobi equations on the network and we study related comparison principles. Under suitable assumptions, we prove in particular that the value function is the unique constrained viscosity solution of the Hamilton-Jacobi equation on the network.

MSC:

35R02 PDEs on graphs and networks (ramified or polygonal spaces)
35F21 Hamilton-Jacobi equations
35Q93 PDEs in connection with control and optimization
49J15 Existence theories for optimal control problems involving ordinary differential equations
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