Due to concentration and temperature differences across an exothermic autocatalytic traveling front, Rayleigh-Taylor or
double-diffusive instabilities can develop when the front travels in a Hele-Shaw cell oriented vertically in the gravity field. In thin
layers of solution in contact with air, surface tension effects can in addition come into play. Our research aims at a theoretical
understanding of the spatio-temporal dynamics resulting from the coupling between these various hydrodynamic instabilities with the
autocatalytic reactions.