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. 
@article{FAA_2015_49_4_a7,
     author = {S. V. Zakharov},
     title = {Singularities of~$A$ and~$B$ {Types} in {Asymptotic} {Analysis} of {Solutions} of a {Parabolic} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--85},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_4_a7/}
}
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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/