On the existence of transition layers of spike type in reaction–diffusion–convection equations

We investigate steady state solutions to a class of systems of reaction–diffusion–convection equations with small diffusion and small convection in case of a scalar spatial variable. Our main concern is to prove the existence of a solution with an interior layer of spike type for higher order systems without taking into consideration the influence of boundary conditions. To this end we combine two methods of the theory of singular perturbations: the method of integral manifolds and the method of boundary layer functions.