  This is the first part of our study of inertial manifolds for the system of
1D reaction-diffusion-advection equations which is devoted to the case of
Dirichlet or Neumann boundary conditions. Although this problem does not
initially possess the spectral gap property, it is shown that this property is
satisfied after the proper non-local change of the dependent variable. The case
of periodic boundary conditions where the situation is principally different
and the inertial manifold may not exist is considered in the second part of our
study.

Analysis of PDEs