Continuous solution for a non-linear eikonal system

Ahmad El Hajj; Aya Oussaily

doi:10.3934/cpaa.2021131

Article Contents

2021, Volume 20, Issue 11: 3795-3823. Doi: 10.3934/cpaa.2021131 open access

This issue Previous Article Existence and multiplicity for Hamilton-Jacobi-Bellman equation Next Article Global boundedness of radial solutions to a parabolic-elliptic chemotaxis system with flux limitation and nonlinear signal production

Continuous solution for a non-linear eikonal system

Ahmad El Hajj^, and
Aya Oussaily

Université de Technologie de Compiègne, LMAC, 60205 Compiègne Cedex, France

^* Corresponding author
^* Corresponding author

Received: December 2020

Revised: June 2021

Early access: July 2021

Published: November 2021

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Abstract

In this work, we are dealing with a non-linear eikonal system in one dimensional space that describes the evolution of interfaces moving with non-signed strongly coupled velocities. We prove a global existence result in the framework of continuous viscosity solution. The approach is made by adding a viscosity term and passing to the limit for vanishing viscosity, relying on a new gradient entropy and $ BV $ estimates. A uniqueness result is also proved through a comparison principle property.

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Mathematics Subject Classification: 35A01, 35D40, 35F20, 35F21, 35F50, 35L40, 35Q35, 74H20.

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