Geodesic
On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1267-1276

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A complete asymptotic expansion of the solution to an initial value problem for a singularly perturbed system of hyperbolic equations is constructed and justified. A specific feature of the problem is that its solution has a wavelet zone in a neighborhood of which the asymptotics is described by a parabolic equation. 
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     author = {A. V. Nesterov},
     title = {On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1267--1276},
     publisher = {mathdoc},
     volume = {52},
     number = {7},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_7_a8/}
}
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A. V. Nesterov. On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1267-1276. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_7_a8/