# Asymptotic Expansion of the Solution to a Partially Dissipative System of Equations with a Multizone Boundary Layer

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### Abstract

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.

## Keywords:

singularly perturbed partially dissipative system of equations multiple root of a degenerate equation multizone boundary layer## Notes

### FUNDING

This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00424.

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