Abstract
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 A3 and the boundary singularity of type B3. For another choice of the initial function, singular points corresponding to A2n+1 and B2n+1 with arbitrary n ≥ 1 are obtained.
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