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In this paper, we study solutions for a weakly coupled system of eikonalequations arising in an optimal path-planning problem for autonomous vehicles.The model considered takes into account the possibility of two types ofbreakdown, partial and total, which happen at a known, spatially inhomogeneousrate. In particular, we show how to bypass the delicate degenerate couplingcondition by using existing results on weakly coupled systems of HamiltonJacobi equations. Then we consider finite element method schemes built forconvection-diffusion problems to construct approximate solutions for thissystem and produce some numerical simulations.

Weakly coupled systems of eikonal equations for autonomous vehicles