Geodesic
Asymptotic solution of a Cauchy problem in a neighbourhood
Sbornik. Mathematics, Tome 197 (2006) no. 6, pp. 835-851 
S. V. Zakharov. Asymptotic solution of a Cauchy problem in a neighbourhood. Sbornik. Mathematics, Tome 197 (2006) no. 6, pp. 835-851. http://geodesic.mathdoc.fr/item/SM_2006_197_6_a2/
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     author = {S. V. Zakharov},
     title = {Asymptotic solution of a {Cauchy} problem in a neighbourhood},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_6_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The existence of an asymptotic solution of a quasilinear parabolic equation with a small parameter is proved in a neighbourhood of the transition point of a weak discontinuity of the solution of the limiting equation into a shock wave. The behaviour of the first two coefficients of this asymptotic solution is studied in the entire plane of the stretched variables. Bibliography: 4 titles.

[1] S. V. Zakharov, A. M. Ilin, “Ot slabogo razryva k gradientnoi katastrofe”, Matem. sb., 192:10 (2001), 3–18 | MR | Zbl

[2] A. M. Ilin, Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, Fizmatlit, M., 1989 | MR | Zbl

[3] V. G. Sushko, “Ob asimptoticheskikh razlozheniyakh reshenii odnogo parabolicheskogo uravneniya s malym parametrom”, Differents. uravneniya, 21:10 (1985), 1794–1798 | MR | Zbl

[4] N. N. Lebedev, Spetsialnye funktsii i ikh prilozheniya, Fizmatgiz, M., L., 1963 | MR | Zbl