In this paper, a multi-layered interface system is introduced, which is formally derived by a singular limit of a weakly coupled system of the Allen–Cahn type equation. By using the level set approach, this system is written as a quasi-monotone degenerate parabolic system with discontinuous functions. The well-posedness of viscosity solutions is shown, and the singularity of particular viscosity solutions is discussed.
Cite this article
Hiroyoshi Mitake, Hirokazu Ninomiya, Kenta Todoroki, A level set approach for multi-layered interface systems. Interfaces Free Bound. 22 (2020), no. 4, pp. 383–400DOI 10.4171/IFB/444