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

Article type: Research Article

Authors: Schneider, Klaus R. | Vasil'eva, Adelaida B.

Affiliations: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany E‐mail: schneide@wias‐berlin.de | Department of Mathematics, Faculty of Physics, Moscow State University, 119899 Moscow, Russia E‐mail: abvas@mathabv.phys.msu.su

Abstract: 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.

Keywords: reaction–diffusion–convection equations, contrast structures of spike type, singular perturbations, asymptotic expansions, boundary layer functions, integral manifolds

Journal: Asymptotic Analysis, vol. 25, no. 3-4, pp. 183-199, 2001