A kinetic eikonal equation

Details A kinetic eikonal equation A kinetic eikonal equation

2012-02-10

arxiv.org/abs/1202.2342v1

Mathematics

Analysis of PDEs

Scientific paper

We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit $(t,x)\to (t/\eps,x/\eps)$. 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.

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