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Asymptotic expansions for hyperbolic–parabolic systems with a small parameter

✍ Scribed by Gunilla Kreiss

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
835 KB
Volume
13
Category
Article
ISSN
0170-4214

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✦ Synopsis

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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This work is concerned with asymptotic properties of solutions to forward equations for singularly perturbed Markov chains with two small parameters. It is motivated by the model of a cost-minimizing firm involving production planning and capacity expansion and a two-level hierarchical decomposition