Stability of traveling front solutions with algebraic spatial decay for some autocatalytic chemical reaction systems (Q2902728)

The paper reports results for traveling-front solutions of the following reaction-diffusion system for concentrations of a reactant, \(u\), and a catalyst, \(v\): NEWLINE\[NEWLINE\begin{aligned} & u_t = d\Delta u -u^qv^p,\\ &v_t = \Delta v +u^qv^p,\end{aligned} NEWLINE\]NEWLINE with \(p,q>1\). The existence and stability of traveling fronts is proved for solutions traveling with velocities exceeding a certain critical value. Tails of such solutions decay not exponentially, but as power functions of the coordinate. The Evans-function method is employed for the stability analysis.