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$ BV $ solution for a non-linear Hamilton-Jacobi system

  • * Corresponding author: Ahmad El Hajj

    * Corresponding author: Ahmad El Hajj 
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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. For such kind of systems, previous results on the existence and uniqueness are available for quasi-monotone systems and other special systems in Lipschitz continuous space. It is worth mentioning that our system includes, in particular, the case of non-decreasing solution where some existence and uniqueness results arose for strictly hyperbolic systems with a small total variation. In the present paper, we consider initial data with unnecessarily small $ BV $ seminorm, and we use some $ BV $ bounds to prove a global-in-time existence result of this system in the framework of discontinuous viscosity solution.

    Mathematics Subject Classification: 58F15, 58F1735A01, 74G25, 35F20, 35F21, 35L40, 35Q35, 35D40.


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