Asymptotic solution of a Hamilton–Jacobi equation

Abstract

This paper is concerned with the asymptotic behaviour of the solution of a first order Hamilton-Jacobi type equation which models the propagation of a front in a medium with a periodic spatial inhomogeneity, characterised by a speed parameter R₀. We are interested in the behaviour of the solution for large time and when the spatial period tends to zero. We find that such an equation leads to an asymptotic speed which, surprisingly enough, is independent of the cell variation of the parameter R₀, but equals the maximum value of this parameter.