Singularities of A and B types in asymptotic analysis of solutions of a parabolic equation

摘要

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 a parts per thousand yen 1 are obtained.