Traveling Wave Solutions To A Reaction-Diffusion System From Combustion Theory

  • Smail Djebali


In this paper, we are concerned with the existence of traveling wave solutions to a system of reaction-diffusion equations. The latter describes the propagation of evolving fronts for a two-step chemical reaction. With the resulting system of two second order ODEs, three different limit conditions may be taken into account at positive infinity. For each case, we prove existence of bounded solutions on $(0,\infty)$ for any value of the wave speed; the analysis includes the case where one of the coefficients vanishes. Then we show that such solutions can be extended to the negative half-line to get unbounded solutions. Shooting type techniques, upper and lower solution method as well as fixed point arguments and Leray-Schauder topological degree are used.