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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2006 Volume 197, Number 6, Pages 47–62 (Mi sm1574)

This article is cited in 7 papers

Asymptotic solution of a Cauchy problem in a neighbourhood of a gradient catastrophe

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: 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.

UDC: 517.95

MSC: 35B40, 35K60

Received: 16.12.2004

DOI: 10.4213/sm1574


 English version:
Sbornik: Mathematics, 2006, 197:6, 835–851

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© Steklov Math. Inst. of RAS, 2026