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.
\Bibitem{Zak06}
\by S.~V.~Zakharov
\paper Asymptotic solution of a Cauchy problem in a neighbourhood
of a gradient catastrophe
\jour Sb. Math.
\yr 2006
\vol 197
\issue 6
\pages 835--851
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Linking options:
https://www.mathnet.ru/eng/sm1574
https://doi.org/10.1070/SM2006v197n06ABEH003780
https://www.mathnet.ru/eng/sm/v197/i6/p47
This publication is cited in the following 7 articles:
S. V. Zakharov, “Solution of a Parabolic Hamilton–Jacobi Type Equation Determined by a Simple Boundary Singularity”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S257–S269
S. V. Zakharov, “Singular points and asymptotics in the singular Cauchy problem for the parabolic equation with a small parameter”, Comput. Math. Math. Phys., 60:5 (2020), 821–832
Sergey V. Zakharov, “Asymptotic solutions of a parabolic equation near singular points of A and B types”, Ural Math. J., 5:1 (2019), 101–108
A. R. Danilin, S. V. Zakharov, O. O. Kovrizhnykh, E. F. Lelikova, I. V. Pershin, O. Yu. Khachai, “Ekaterinburgskoe nasledie Arlena Mikhailovicha Ilina”, Tr. IMM UrO RAN, 23, no. 2, 2017, 42–66
S. V. Zakharov, “Singulyarnye asimptotiki v zadache Koshi dlya parabolicheskogo uravneniya s malym parametrom”, Tr. IMM UrO RAN, 21, no. 1, 2015, 97–104
S. V. Zakharov, “Singularities of A and B Types in Asymptotic Analysis of Solutions of a Parabolic Equation”, Funct. Anal. Appl., 49:4 (2015), 307–310
S. V. Zakharov, “A construction of a solution to the Burgers equation with a specified asymptotics”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S243–S249
Citation in format AMSBIB
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