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A hyperbolic singular perturbation of Burgers' equation

✍ Scribed by Benjamin F. Esham Jr.

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
524 KB
Volume
12
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

This paper is concerned with the effect of perturbing Burgers' equation by a small term ϵ^2^ U~tt~. It is shown by means of an energy estimate that the solution of Burgers' equation provides a uniform O (ϵ) approximation of the solution of the full hyperbolic problem. Existence and uniqueness of classical solutions for both problems is proved. A related linear problem is first addressed using the Faedo–Galerkin method to obtain key estimates. Important for the hyperbolic problem is the introduction of an ϵ‐dependent energy in order to track the order‐ϵ behaviour of various higher‐order derivatives. Subsequent use of Schauder technique and Banach contraction mapping principle yields solutions of the semilinear problems.

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