A Transmission Strategy for Hyperbolic Internal Waves of Small Width

Olivier Gues[1]; Jeffrey Rauch[2]

  • [1] Université de Provence, Marseille, France
  • [2] University of Michigan, Ann Arbor MI, USA

Séminaire Équations aux dérivées partielles (2005-2006)

  • Volume: 2005-2006, page 1-9

Abstract

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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.

How to cite

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Gues, Olivier, and Rauch, Jeffrey. "A Transmission Strategy for Hyperbolic Internal Waves of Small Width." Séminaire Équations aux dérivées partielles 2005-2006 (2005-2006): 1-9. <http://eudml.org/doc/11125>.

@article{Gues2005-2006,
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.},
affiliation = {Université de Provence, Marseille, France; University of Michigan, Ann Arbor MI, USA},
author = {Gues, Olivier, Rauch, Jeffrey},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {discontinuous source terms; piecewise smooth solutions; thin layers; transmission problem strategy; overdetermined equations for correctors},
language = {eng},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {A Transmission Strategy for Hyperbolic Internal Waves of Small Width},
url = {http://eudml.org/doc/11125},
volume = {2005-2006},
year = {2005-2006},
}

TY - JOUR
AU - Gues, Olivier
AU - Rauch, Jeffrey
TI - A Transmission Strategy for Hyperbolic Internal Waves of Small Width
JO - Séminaire Équations aux dérivées partielles
PY - 2005-2006
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2005-2006
SP - 1
EP - 9
AB - 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.
LA - eng
KW - discontinuous source terms; piecewise smooth solutions; thin layers; transmission problem strategy; overdetermined equations for correctors
UR - http://eudml.org/doc/11125
ER -

References

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