@Article{IJNAM-10-99,
author = {Clain , S. and Djenno Ngomanda , M.},
title = {The Half-Planes Problem for the Level Set Equation},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {1},
pages = {99--115},
abstract = {<p style="text-align: justify;">The paper is dedicated to the construction of an analytic solution for
the level set equation in $R^2$ with an initial condition constituted by two half-planes.
Such a problem can be seen as an equivalent Riemann problem in the Hamilton-Jacobi
equation context. We first rewrite the level set equation as a non-strictly hyperbolic
problem and obtain a Riemann problem where the line sharing the initial discontinuity
corresponds to the half-planes junction. Three different solutions corresponding to a
shock, a rarefaction and a contact discontinuity are given in function of the two half-planes
configuration and we derive the solution for the level set equation. The study
provides theoretical examples to test the numerical methods approaching the solution of
viscosity of the level set equation. We perform simulations to check the three situations
using a classical numerical method on a structured grid.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/560.html}
}