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

TL;DR

This paper constructs asymptotic solutions near large-gradient and Lagrange singularities of A-type in a quasilinear parabolic equation, providing insights into shock wave formation in viscous media.

Contribution

It introduces a method to analyze asymptotic solutions near singularities in quasilinear parabolic equations with small viscosity.

Findings

Asymptotic solutions are constructed near singularities.

Insights into shock wave formation in viscous media.

Analysis of large-gradient and Lagrange singularities.

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.