Asymptotic expansions for hyperbolic–parabolic systems with a small parameter

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Abstract
In this paper we consider initial‐boundary value problems for systems with a small parameter ϵ. The problems are mixed hyperbolic–parabolic when ϵ > 0 and hyperbolic when ϵ = 0. Often the solution can be expanded asymptotically in ϵ and to first approximation it consists of the solution of the corresponding hyperbolic problem and a boundary layer part. We prove sufficient conditions for the expansion to exist and give estimates of the remainder. We also examine how the boundary conditions should be choosen to avoid O(1) boundary layers.

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