Discontinuous solutions of Hamilton-Jacobi equations on networks *

Abstract : This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as solution to a system of Hamilton-Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.
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Submitted on : Saturday, September 10, 2016 - 5:20:49 PM
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Philip Jameson Graber, Cristopher Hermosilla, Hasnaa Zidani. Discontinuous solutions of Hamilton-Jacobi equations on networks *. Journal of Differential Equations, Elsevier, 2017, 263 (12), pp.8418-8466. ⟨10.1016/j.jde.2017.08.040⟩. ⟨hal-01363628⟩

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