Asymptotic expansion of the solution to a partially dissipative system of equations with a multizone boundary layer

An asymptotic expansion with respect to a small parameter is constructed and proved for the solution of the boundary value problem for a singularly perturbed stationary partially dissipative system of equations in the case when one of the equations of the degenerate system has a double root. The multiplicity of this root leads to a multizone boundary layer, so the standard algorithm for constructing an asymptotic expansion of a boundary-layer solution becomes insufficient and requires a substantial modification. The constructed asymptotic expansion is substantiated using the asymptotic method of differential inequalities.