Weakly coupled systems of eikonal equations for autonomous vehicles

Maria Teresa Chiri; Kenneth D Czuprynski; Ludmil T Zikatanov

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arXiv · 2310.02966

Weakly coupled systems of eikonal equations for autonomous vehicles

Maria Teresa Chiri·Kenneth D Czuprynski·Ludmil T Zikatanov

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Abstract

In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem with random breakdown. The model considered takes into account two types of breakdown for the vehicle, partial and total, which happen at a known, spatially inhomogeneous rate. In particular, we analyze the complications due to the delicate degenerate coupling condition by using existing results on weakly coupled systems of Hamilton-Jacobi equations. Then we consider finite element method schemes built for convection-diffusion problems to construct approximate solutions for this system and produce some numerical simulations.

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Maria Teresa Chiri, Kenneth D Czuprynski, Ludmil T Zikatanov. 2023-10-04. Weakly coupled systems of eikonal equations for autonomous vehicles. https://arxiv.org/abs/2310.02966

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