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Séminaire Équations aux dérivées partielles (Polytechnique)

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Olivier Gues; Jeffrey Rauch
A Transmission Strategy for Hyperbolic Internal Waves of Small Width
Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Exp. No. 13, 9 p.
Article PDF | Reviews MR 2276078

Résumé - Abstract

Semilinear hyperbolic problems with source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source in the limit of thin layers. The key idea is to use a transmission problem strategy for the problem with the smooth internal layer. That leads to an ansatz different from the obvious candidates. The obvious candidates lead to overdetermined equations for correctors. With the transmission problem strategy we compute infinitely accurate expansions.

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