Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion

الأصل · EN

We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of Inertial Confinement Fusion. We show that solutions of the Cauchy problem with physically relevant initial data become planar exponentially fast with rate s(',k)>0, where '=TminTmax≪ 1 is a small temperature ratio and k≫ 1 the transversal wrinkling wavenumber of perturbations. We rigorously recover in some particular limit (',k)→ (0,+∞) a dispersion relation s(',k) γ₀ kα previously computed heuristically and numerically in some physical models of Inertial Confinement Fusion.