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September  2019, 8(3): 543-565. doi: 10.3934/eect.2019026

## A comparison principle for Hamilton-Jacobi equation with moving in time boundary

 1 Normandie Univ, INSA de Rouen, LMI (EA 3226 - FR CNRS 3335), 76000 Rouen, France 2 685 Avenue de l'Université, 76801 St Etienne du Rouvray cedex, France

Received  May 2018 Revised  November 2018 Published  May 2019

In this paper we consider an Hamilton-Jacobi equation on a moving in time domain. The boundary is described by a $C^{1}$ function. We show how we derive this equation from the work of [26]. We only prove a comparison principle since the proof of other theoritical results can be found in [20]. At the end of the paper, we consider a short homogenization result in order to reinforce the traffic flow interpretation of the equation.

Citation: Nicolas Forcadel, Mamdouh Zaydan. A comparison principle for Hamilton-Jacobi equation with moving in time boundary. Evolution Equations & Control Theory, 2019, 8 (3) : 543-565. doi: 10.3934/eect.2019026
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