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.
@article{SEDP_2005-2006____A13_0,
author = {Gues, Olivier and Rauch, Jeffrey},
title = {A {Transmission} {Strategy} for {Hyperbolic} {Internal} {Waves} of {Small} {Width}},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:13},
pages = {1--9},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2005-2006},
mrnumber = {2276078},
language = {en},
url = {http://www.numdam.org/item/SEDP_2005-2006____A13_0/}
}
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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:13 PY - 2005-2006 SP - 1 EP - 9 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2005-2006____A13_0/ LA - en ID - SEDP_2005-2006____A13_0 ER -
%0 Journal Article %A Gues, Olivier %A Rauch, Jeffrey %T A Transmission Strategy for Hyperbolic Internal Waves of Small Width %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:13 %D 2005-2006 %P 1-9 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2005-2006____A13_0/ %G en %F SEDP_2005-2006____A13_0
Gues, Olivier; Rauch, Jeffrey. A Transmission Strategy for Hyperbolic Internal Waves of Small Width. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 13, 9 p. http://www.numdam.org/item/SEDP_2005-2006____A13_0/
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