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Continuous solution for a non-linear eikonal system

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  • 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.

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


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