The paper “Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions” co-authored by Anna Kostianko and Sergey Zelik, has been published in Communications in Pure and Applied Analysis.  The paper is the first part of their study of inertial manifolds for systems of reaction-diffusion-advection equations in one space dimension, and covers the case of Dirichlet or Neumann boundary conditions. A link the published version of the paper is here.