Traveling fronts for the thermo-diffusive system with arbitrary Lewis numbers
The paper deals with a reaction-diffusion system of a special type, namely, of so-called KPP type. The definition domain of the system is cylindrical. The right hand side of the system contains a Lewis number, which is the ratio of thermal and material diffusivities. The main goal of the work is to show that traveling fronts solutions exist for all Lewis numbers and approach uniform limits at the two ends of the cylinder. To substantiate this result, the authors construct the KPP traveling wave using the standard procedure of restricting the problem to a finite cylinder and then passing to the limit of an infinite cylinder. The presumed absence of cellular instabilities in the KPP case makes the proof work from the physical point of view.
scientific article; zbMATH DE number 5731003
scientific article