We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t, x) → (t/ε, x/ε). 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 sol...

We derive next-to-eikonal (NEik) corrections to the background quark propagator, which stem from (i) considering a finite longitudinal width target instead of an infinitely thin shockwave and (ii) including interaction with transverse components field. These two different eikonal approximation combine together provide gauge covariant expression for propagator at NEik accuracy. then apply our re...

Fast Marching represents a very efficient technique for solving front propagation problems, which can be formulated as partial differential equations with Dirichlet boundary conditions, called Eikonal equation: