# 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

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topGues, 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 -

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