WIAS Preprint No. 170, (1995)

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



Authors

  • Schneider, Klaus R.
  • Vasil´eva, Adelaida B.

2010 Mathematics Subject Classification

  • 35K55 35B25 34D15 34E05

Keywords

  • Reaction-diffusion-convection equations, contrast structures of spike type, singular perturbations, asymptotic expansions, boundary layer functions, integral manifolds

Abstract

We investigate steady state solutions to a class of systems of reaction-diffusion-convection equations with small diffusion and small convection, and which depend on one space 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.

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