Geodesic
Singularities of~$A$ and~$B$ Types in Asymptotic Analysis of Solutions of a Parabolic Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 4, pp. 82-85.

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The Cauchy problem for a quasi-linear parabolic equation with a small parameter multiplying a higher derivative is considered in two cases where the solution of the limit problem has a point of gradient catastrophe. The integrals determining the leading approximation correspond to the Lagrange singularity of type $A_3$ and the boundary singularity of type $B_3$. For another choice of the initial function, singular points corresponding to $A_{2n+1}$ and $B_{2n+1}$ with arbitrary $n\ge 1$ are obtained.
Mots-clés : parabolic equation
Keywords: asymptotics, singular points. 
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S. V. Zakharov. Singularities of~$A$ and~$B$ Types in Asymptotic Analysis of Solutions of a Parabolic Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 4, pp. 82-85. http://geodesic.mathdoc.fr/item/FAA_2015_49_4_a7/

[1] V. I. Arnold, Osobennosti kaustik i volnovykh frontov, Fazis, M., 1996 | MR

[2] I. A. Bogaevskii, Algebra i analiz, 1:4 (1989), 1–16 | MR

[3] B. Khesin, G. Misiołek, Trudy MIAN, 259 (2007), 77–85 | MR

[4] A. M. Ilin, Dokl. AN SSSR, 283:3 (1985), 530–534 | MR | Zbl

[5] V. I. Arnold, Funkts. analiz i ego pril., 6:4 (1972), 3–25 | DOI | MR

[6] S. V. Zakharov, A. M. Ilin, Matem. sb., 192:10 (2001), 3–18 | DOI | MR | Zbl

[7] S. V. Zakharov, Matem. sb., 197:6 (2006), 47–62 | DOI | MR | Zbl

[8] V. I. Arnold, UMN, 33:5 (1978), 91–105 | MR | Zbl