JournalsifbVol. 22, No. 4pp. 383–400

A level set approach for multi-layered interface systems

  • Hiroyoshi Mitake

    University of Tokyo, Japan

  • Hirokazu Ninomiya

    Meiji University, Tokyo, Japan

  • Kenta Todoroki

    Hitachi Ltd, Tokyo, Japan
A level set approach for multi-layered interface systems cover

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Abstract

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. 383–400

DOI 10.4171/IFB/444