Large-gradient and Lagrange singularities of solutions of a quasilinear parabolic equation

Abstract

Asymptotic solutions of a quasilinear parabolic equation with a small parameter at the higher derivative are constructed near large-gradient and Lagrange singularities of A-type, which represent interest for studying processes of shock waves formation in physical media with a small nonzero viscosity.

arXiv commentKeywords: parabolic equation, Burgers equation, Cole-Hopf transform, asymptotics, large gradient, Lagrange singularities, Whitney fold. 7 pages