Relaxation to equilibrium in diffusive-thermal models with a strongly varying diffusion length-scale (Q390235)

The paper considers reaction-diffusion equations with a strongly varying diffusion length-scale. More precisely, the mathematical model under consideration, written in non-dimensional form, is: NEWLINE\[NEWLINE\begin{gathered} \left(\frac{1}{T}\right)^n T_t-div(\lambda(T)\nabla(T))+CT_x=F(T), \,t>0,\, (x,y)\in {\mathbb R}\times {\mathbb R},\\ T(t,-\infty, y)=\varepsilon ', \;\; T(t,+\infty, y)=1, \;\; T(t,x,y+\frac{2\pi}{k})=T(t,x,y),\end{gathered}NEWLINE\]NEWLINE where \(T\) is the reduced temperature scaled by its maximum value at the hot side, \(0\leq \varepsilon '<1\), and \(F(T)\) is a nonlinear term describing the heat release rate. The model under study is relevant in the description of the ablation fronts encountered in inertial confinement fusion, when the hydrodynamical effects are neglected. The authors provide a mathematical study of the relaxation towards the steady planar solution in the context of infinitesimal disturbances whose wavelength is much shorter than the total thickness of the wave.