Abstract: In this talk, we want to study some scalar conservation laws with a non-local flow corresponding to various phenomena in pedestrians' dynamics. After presenting these models and their motivations, we will develop our main tool, which is a stability estimate in L1 of the solutions of scalar conservation laws when the flow and source vary. This estimate is obtained from the Kruzkov doubling variable method and recovers previous estimates, obtained in some particular cases. Then, we can obtain existence and uniqueness for our non-local models by application of the Banach fixed point Theorem. We conclude this talk by giving some qualitative properties of the models and some modelisation's issues.

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