A kinetic eikonal equation
Analysis of PDEs
2012-02-13 v1
Abstract
We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit . We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small diffusivity. We prove well-posedness of the phase problem and convergence towards the viscosity solution of the Hamilton-Jacobi equation. This is a preliminary work before analysing the propagation of reaction fronts in kinetic equations.
Keywords
Cite
@article{arxiv.1202.2342,
title = {A kinetic eikonal equation},
author = {Emeric Bouin and Vincent Calvez},
journal= {arXiv preprint arXiv:1202.2342},
year = {2012}
}