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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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