Solitary traveling waves in a heterogeneous medium with a chemical reaction

A correct method for constructing autowave solutions is proposed for single-temperature models of unsteady processes in a dissipative medium with Arrhenius type chemical reactions. It is based on extending the temperature range to 0 K and using the Kolmogorov–Petrovskii–Piskunov approach. Solutions that are not inconsistent with the Nernst theorem are selected from the obtained finite spectrum of autowave solutions. For a quasihomogeneous model of gas filtration in a dissipative heterogeneous medium with a single irreversible chemical reaction, such an autowave solution is unique. A nondimensional parameter is found whose critical value for the selected Zel’dovich number defines the existence condition for this self-similar solution. A criterion is obtained for the initial temperature range in which the chemical transformations in the reaction are negligibly small for autowave processes.