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

Nicolas Forcadel; Mamdouh Zaydan

doi:10.3934/eect.2019026

Article Contents

2019, Volume 8, Issue 3: 543-565. Doi: 10.3934/eect.2019026

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

Nicolas Forcadel^1,2, , and
Mamdouh Zaydan^1,2,

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: April 30, 2018

Revised: October 31, 2018

Early access: May 2019

Published: August 2019

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Abstract

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.

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Mathematics Subject Classification: 35D40, 90B20, 35B27, 35F20, 45K05.

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References

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